• <tr id="yyy80"></tr>
  • <sup id="yyy80"></sup>
  • <tfoot id="yyy80"><noscript id="yyy80"></noscript></tfoot>
  • 99热精品在线国产_美女午夜性视频免费_国产精品国产高清国产av_av欧美777_自拍偷自拍亚洲精品老妇_亚洲熟女精品中文字幕_www日本黄色视频网_国产精品野战在线观看 ?

    Novel soliton molecule solutions for the second extend (3+1)-dimensional Jimbo-Miwa equation in fluid mechanics

    2023-12-28 09:20:08HongcaiMaXiaoyuChenandAipingDeng
    Communications in Theoretical Physics 2023年12期

    Hongcai Ma,Xiaoyu Chen and Aiping Deng

    Department of Applied Mathematics,Donghua University,Shanghai 201620,People’s Republic of China

    Abstract The main aim of this paper is to investigate the different types of soliton molecule solutions of the second extend (3+1)-dimensional Jimbo-Miwa equation in a fluid.Four different localized waves:line solitons,breather waves,lump solutions and resonance Y-type solutions are obtained by the Hirota bilinear method directly.Furthermore,the molecule solutions consisting of only line waves,breathers or lump waves are generated by combining velocity resonance condition and long wave limit method.Also,the molecule solutions such as line-breather molecule,lumpline molecule,lump-breather molecule,etc.consisting of different waves are derived.Meanwhile,higher-order molecule solutions composed of only line waves are acquired.

    Keywords: second extend(3+1)-dimensional Jimbo-Miwa equation,N-soliton solution,velocity resonance,soliton molecule solution

    1.Introduction

    The study of analytical solutions helps us to clarify the physical properties and behaviour of nonlinear equations,which are structural models for many physical phenomena[1].There are a number of theoretical approaches to solving analytical solutions,such as the tanh-coth method [2–4],Riemann–Hilbert method[5–7],the inverse scattering method[8,9],Darboux transformation method [10–13],the Painlevé analysis [14],the generalized symmetry method [15],Hirota bilinear method [16,17,38] and others [18–21].

    In the subject area of the natural sciences,solitons demonstrate remarkable order in the presence of nonlinear effects.In general,we refer to a wave that retains its original size,shape and direction during motion or propagation,and has stability,as a soliton wave [22].In recent years,a new topic soliton molecules has emerged in the study of solitons,which are bound states of one or more solitons [23–27,41–43].The three well-known local waves: lump waves,breathers and line waves are very significant components of soliton molecule solutions.

    The (3+1)-dimensional Jimbo-Miwa equation

    first introduced by Jimbo and Miwa [28] is the second equation of the KP hierarchy.This equation is used to describe certain interesting (3+1)-dimensional waves in physics and then discussed by many authors on its solutions[29],integrability properties[30],symmetries[31–33]and so on.Wazwaz have proposed two extended (3+1)-dimensional Jimbo-Miwa (3D-eJM) equations [34].The second 3D-eJM equation is deduced by replacinguytwithuxt+uyt+uztas

    where u=u(x,y,z,t)is a function with respect to three spatial coordinates x,y,z and temporal variable t which indicates the amplitude of the wave in the physics of fluids,especially in ocean engineering and science [1].Although equation (2)belongs to the Kadomtsev–Petviashvili hierarchy,but it does not satisfy the classical productability condition [28].

    Figure 2.Double soliton solution to the 3D-eJM equation with p1=1,q1=1,r1=2,p2=2,q2=4,r2=1,φ1=φ2=0,z=0 in equation (10).

    In contrast to other 3D-eJM equation,relatively little research has been done on this equation.For equation (2),Wazwaz derived multiple soliton solutions [34],Guo et al presented four different localized waves and interaction solutions between lump solutions,line solitons,breathers and rogue waves using the Hirota bilinear method,Sun et al found lump and lump-kink solution [36],Xu et al constructed the resonance behavior with the aid of special parameter restrictions[37].But as far as we know,no molecule solution of this equation has been studied,especially for the lump molecule solution,a special structural phenomenon that does not exist in most (2+1)-dimensional physical models by using long wave limit method [38,39].All of findings in this paper can be used to explain some natural phenomena in the ocean waves and nonlinear optics.Further,the study can be extended to investigate several other nonlinear systems to understand the physical insights of the molecule phenomenon in their dynamics.

    This paper has following structure.In section 2,we give four different types of localized waves and the expression of their velocity through the use of N-soliton solution,module and velocity resonance conditions,long wave limit method.We present three molecule solutions consisting of the same localized wave e.g: line molecule,breather molecule and lump molecule solution in section 3.In section 4,a number of molecule solutions with a mixture of different localized waves are obtained.And two forms of the higher order line molecule solutions are derived.Some conclusions and discussions are given in section 5.

    2.Different localized waves to the second 3D-eJM equation

    According to the Hirota bilinear method and Bell polynomial technique,with logarithmic transform

    the equation (2) can be converted to following bilinear form:

    where operators Dx,Dtare defined by

    To facilitate mathematical calculations,the equation (4) can be expanded as

    The N order solution of equation (4) has the following form:

    where

    Figure 3.First order line breather solution to the 3D-eJM equation with=2 +i,φ1=φ2=0,z=0 in equation (6).

    Here,pk,qk,rk,φk(k=1,2,…,N) are arbitrary constants,Σμ=0,1denotes all combinations of μk=0 or 1.The N-soliton solution of equation(2)can be expressed through substituting equation (6) into equation (3).Based on the N-soliton solution,we construct a number of different localized waves.

    Figures 1(a),(b) depicts the 3D-plot and density plot of single line soliton with parameters p1=1,q1=1,r1=2,φ1=0 at z=0 plane.Subject to this parameter,equation (3)is reduced to

    Actually the ratio of p1to-q1determines the slope of the line in figure 1(b),φ1affects the initial position (t=0) of the solution in the diagram.In other words,if φ1is not equal to zero,then the centre of the solution at the initial position must not pass through (0,0) at z=0.In order to better study the motion of line wave,we decompose the velocity of the solution orthogonally in the x,y perpendicular directions and give its expression as follows

    whereωksatisfies equation (7).The velocity of single line wave in equation (8) is.The correctness of the above assertion can be demonstrated in figure 1(b).

    Double soliton solution can be seen as a morphism consisting of the nonlinear superposition of two single soliton solutions.Its kinematic process can be split into two mutually independent single line wave motions and its velocity can be elaborated by two velocity expressions in equation (9).This also indicates that the collision between two soliton waves is elastic: the velocity,phase shift and amplitude do not change before or after the collision.With p1=1,q1=1,r1=2,p2=2,q2=4,r2=1,φ1=φ2=0,a double soliton solution to the 3D-eJM equation is presented as

    It can be seen in figure 2 and travels at a speed of

    The N-order breather solution can be obtained by imposing module resonance condition on the parameters of the 2N-order soliton solution,i.e.

    where the symbol ?indicates the complex conjugate number of the parameter.It is similar in nature since the breather solution is derived from the soliton solution.But the pace expression of breather is

    For N=2,second order breather solution can be deduced fromu=2 (l nfx) with

    The N-order lump solution also can be derivated from 2N-order soliton solution.As the procedure for finding the exact solution of lump using the long-wave limit method is well established,we directly provide following constraints:

    Then the N-order lump solution to the 3D-eJM equation can be acquired if we take δ →0,specific forms are

    whereξk,Aks(k,s=1,2,3,4) fulfills the equation (7).The second-order breather solution can similarly be viewed as the interaction situation between two first order ones.In order to clearly show the interaction solution described,we make the directions of motion of the two first order breather solutions orthogonal to each other and show in figure 4.One along thePk,Qk,Rk,φkare arbitrary constants,Φkaffects the initial position of the corresponding lump solution.We usually study the trajectory of the wave crest of the lump wave.According to the solution of the system of equations{ux=0,uy=0},we accquire the velocity formula of lump wave

    negative direction of the y and the other along the negative direction of the x,with velocitiesrespectively.

    When N=1,with specific parameters,the expression of a first order lump wave is reduced as below:

    We put the three-dimensional plot,density plot and sectional plot of the above solution in figure 5.

    When N=2

    whereθk,Bksmeet the equation (16).Second order lump solution can be represented by placing equation (19) in equation (3) as shown in figure 6.We makeφk(k=1,2,3,4) not all zero,allowing us to split the trajectory of the two first order lump solutions.Their speeds arerespectively.

    As we all know that two soliton will transform to resonance Y-type soliton if we take suitablepi,qi,ri(i=1,2) in accordance with exp (Aks)=0and{pk≠psorqk≠qsorrk≠rs}.The speed of Y-type structure solution has rarely been investigated in the previous literature.We likewise provide an expression for its velocity by analysing the variation with time of the position of the intersection point,

    Let N=2,the f is transformed to 2-resonance Y-type solution as

    where ξkare given by equation(7),and this phenomenon can be observed in figure 7.The velocity of above solution is

    Let N=3,with exp(A12)=exp (A13)=0,the f is reduced as

    where ξk,bksare given by equation (7) and equation (13).Substitute equation(22)in equation(3),we achieve two different kinds of 3-resonance Y-type solutions as show in figure 8.One in x-y and z=0 plane,the other is in y-z and x=0 plane.The shape of solution in figure 8(a) is similar to that of X.

    3.Molecules composed of the same waves

    In the last section we focused on four types of local waves and gave expressions for their respective velocities.It is not hard to see from the images of the higher-order solutions that a higher-order solution can be seen as an interaction phenomenon between several lower-order solutions.Much literature shows that collisions between these four local waves are all elastic collisions,the same as between two line waves[44–46].It is well known that assuming that the velocities of the two lower order solutions are identical (including the x,y axes),the two solutions are bound into a new structure during the motion called molecule solution.This section demonstrates several molecule solutions consisting of the same local wave.

    To investigate the single line molecule solution,the fuction f can be choosed as same as second order soliton solution.With the parameters as the figures 9(a)–(c),the u can be unfolded as

    In particular,we find the velocity resonance among two breather waves by picking parameters in equation (13) meet module resonance condition and

    Based the bilinear form,like the lump molecule solution which does not exist in many (2+1)-dimensional integrable models,such as the (2+1)-dimensional generalized Bogoyavlensky–Konopelchenko model [38],Kadomtsev–Petviashvili(KP)system[39],(3+1)-dimensional nagative order KdV-CBS model [47],etc.But for KP systerm,lump molecules can be discovered by using the reduced version of the Grammian form[35,40].With the aid of equation (17),we find the lump molecule solution in equation (2),which needs to cater for

    in equation(19).figure 12 vividly depicts this type of molecule solution with speed,the distance between the centres of two single lump solution is constant.

    4.Molecules made up of the different waves

    In this section,we investigate molecule solutions consisting of different localized waves.It is obvious from the previous analysis that,again,no contact occurs between waves,which remain relatively stationary.The function f can be chosen as

    if we want to look for the line-breather molecule which consisting of a single line and a single wave.ξk,bksare given by equation(7)and(13).Like the one shown in the figure 13,the line wave move parallel to the breather with the same speed.Once the coefficients of x,y,z,t have been determined,φ1,φ3determines the distance between the two solutions.By φ1=φ3,we find a phenomenon shown in figure 14,the breather collides line wave continuously and changes its own form.

    When searching for a molecule solution consisting of lump solution and other solutions,the partial long-wave limit method is required.For example,let

    the lump-line solution will be located on figure 15 with velocity

    When adjusting φ3to 0,the line wave passes exactly through the centre of the lump solution and the two waves merge to form a lump-kink solution.And the lump solution is divided into exactly two section,with the upwardly raised part on top of the kinked area and vice versa.The method used for the idea just mentioned is different from the test We promote on the basis of equation (28) that

    Figure 14.Always collide case with φ1=φ2=φ3=0,other parameters are consistent with figure 13.

    Figure 16.Lump-kink solution to the 3D-eJM equation with Φ3=0,other parameters are consistent with figure 15.

    then the interaction solution between lump and two line waves is derived from weak sense.Another case is that the lump solution and the two line waves as a whole form a molecule solution,i.e.lump-2 line solution.These two cases are shown in figures 17 and 18.The velocity of the molecule solution in both diagrams is,and other line wave is (0,0).

    Since the 2-resonance Y-type solution is derived from the two-soliton solution and we have given lump-2 line molecule in figure 17,it follows that molecule solution consisting of lump solution and 2-resonance Y-type solution must exist in this system.If equation (35) meet the following parameter restrictions

    where ξk,θk,Bks,b34suit equations(7),(13)and(30).On this basis we find two different scenarios.The first case is where the lump solution forms a bound molecule with one of the line waves and moves in the direction in which the other line wave is located.The distance between the lump solution and the two line waves remains fixed,although there is a change in relative position between the two line waves as time changes,and this can be interpreted as a lump-2 line solution in the then it can be denoted as lump-resonance Y-type molecule solution in figure 19.Lump solution is located in the middle of the two branches of the resonance Y-type solution,and the distance between the lump solution and the two branches remains the same from the beginning to the end.This molecule solution is moving at

    If equation (36) meet the module resonance condition and

    where ω3is given by equation (12),then the lump-breather solution is vividly described in figure 20 with

    Since the three branches in the resonance Y-type solution(see figure 7) are not parallel to each other,neither the line wave nor the breather can form molecule solution that never collides with the resonance Y-type solution,but there are cases where they always collide but do not move relative to each other over time.It is sufficient to ensure that the velocities of the resonance Y-type solution and the line wave or breather solution are identical.We can also accquire lumpbreather-line molecule solution by making full use of the conditions (9),(12) and (17) inu=2 (l nfx),where

    In equation (3) and (6),we can obtain integral structure made from lump solution and two resonance Y-type solutions under the following condition

    Here,ξk,θk,Bksare given by equations (7),(13) and (30).It can be seen in figure 21 that lump solution lies between breather and line wave,and the speed is

    where ξk,θk,Bks,bksare given by equation(7),(13)and(30).The two white lines in figure 22 are the trajectories of the two resonance Y-type solutions and the black one is the lump solution.In terms of the positive direction of the x,two resonance Y-type solutions are all the fusion case.The fact that the three lines are parallel means that the lump solution will not collide with the other two solutions,and they have a common velocity.Three trajectories respectively are

    Finally we have generalised the order of the molecule solution consisting of only line waves.On the basis of the specificity expression of the N-order soliton solution (6),the N-line molecule solution has two forms One that we can let arbitrary rkand

    5.Conclusions

    Based on the bilinear form of the second extend (3+1)-dimensional Jimbo-Miwa equation,we concentrate on investigating molecule solution,the bound state that consisting of one or more soliton solutions of the 3D-eJM equation.Through the assistance of long wave limit method,module resonant condition and resonant condition,dynamical features of some one or two order localized waves are presented in figures 1–8.Although we have given an expression for the velocity of each individual localized wave,it should be noted that this is only true for the x–y plane.Of course these expressions can be extended to the x–z or y–z plane by simply replacing the coefficients of x,y in the equation (9),(12) and (20) with coefficients of x,z or y,z simultaneously.In order to achieve the velocity of the lump solution in the x–z or y–z plane,it is sufficient to solve for{ux=0,uz=0},{uy=0,uz=0}respectively.

    With velocity resonance mechanism,a wide range of molecule solutions consisting of line wave,breather wave,lump wave and resonance Y-type solution are graphed in figures 9–24.Particularly the lump-lump molecule in figure 12 which is not common in other low-dimensional physical models.An intersecting rather than parallel line molecule solution with various order are demonstrated in figures 9,23 and 24.We believe that above idea can be applied to other (3+1)-dimensional physical models.These molecule solutions may enlighten our understanding of the phenomenon of nonlinear wave propagation in fluids without collisional patterns.In future work,we are committed to finding new methods that allow us to obtain lump-lump molecule solutions in (2+1)-dimensional productable systems.

    Acknowledgments

    The authors are grateful to the anonymous referees of the journal for helpful comments on an earlier draft.

    Ethical approval

    The authors declare that they have adhered to the ethical standards of research execution.

    Conflict of interest

    The authors declare that there is no conflict of interest regarding the publication of this paper.

    Availability of data and materials

    All data generated or analyzed during this study are included in this published article.

    午夜免费成人在线视频| 久久精品人妻少妇| avwww免费| 久久久久久大精品| 午夜免费激情av| aaaaa片日本免费| 欧美成人免费av一区二区三区| 中文字幕人妻熟人妻熟丝袜美| 亚洲欧美日韩高清在线视频| 在线观看66精品国产| 亚洲乱码一区二区免费版| 88av欧美| 国模一区二区三区四区视频| 欧美高清性xxxxhd video| 免费一级毛片在线播放高清视频| 俄罗斯特黄特色一大片| 少妇裸体淫交视频免费看高清| 麻豆成人午夜福利视频| 国产 一区 欧美 日韩| 熟妇人妻久久中文字幕3abv| 精品人妻偷拍中文字幕| 国产精品,欧美在线| 丝袜美腿在线中文| 成人鲁丝片一二三区免费| 久久人妻av系列| 白带黄色成豆腐渣| 亚洲欧美日韩无卡精品| 淫秽高清视频在线观看| 麻豆成人午夜福利视频| 成人亚洲精品av一区二区| 波多野结衣高清无吗| 免费电影在线观看免费观看| 欧美成人一区二区免费高清观看| 色av中文字幕| 国内精品一区二区在线观看| 人人妻,人人澡人人爽秒播| 99热只有精品国产| 色精品久久人妻99蜜桃| 午夜福利成人在线免费观看| 国产精品一区二区三区四区免费观看 | 国产一区二区三区av在线 | 男女下面进入的视频免费午夜| 噜噜噜噜噜久久久久久91| 午夜精品久久久久久毛片777| 乱码一卡2卡4卡精品| 成人国产综合亚洲| 亚洲精品日韩av片在线观看| 国产一区二区三区在线臀色熟女| 麻豆av噜噜一区二区三区| 天堂av国产一区二区熟女人妻| 国产高清不卡午夜福利| 午夜a级毛片| 校园人妻丝袜中文字幕| 桃色一区二区三区在线观看| 搡老熟女国产l中国老女人| 成人av一区二区三区在线看| 欧美一区二区国产精品久久精品| 午夜激情福利司机影院| 成人一区二区视频在线观看| 日韩一本色道免费dvd| 国产欧美日韩精品亚洲av| 俺也久久电影网| 久久久久久久久久久丰满 | 成年女人永久免费观看视频| 亚洲人成伊人成综合网2020| 国产午夜精品论理片| 神马国产精品三级电影在线观看| 欧美性感艳星| 国产单亲对白刺激| 伦精品一区二区三区| 午夜福利在线在线| 国产一区二区三区在线臀色熟女| 51国产日韩欧美| 99精品在免费线老司机午夜| 99国产极品粉嫩在线观看| 女生性感内裤真人,穿戴方法视频| 最近在线观看免费完整版| 日本一本二区三区精品| 精品不卡国产一区二区三区| 在线免费观看的www视频| 日韩高清综合在线| 精品人妻一区二区三区麻豆 | 亚洲精品一区av在线观看| 成年女人毛片免费观看观看9| 亚洲三级黄色毛片| 亚洲中文字幕一区二区三区有码在线看| 久久精品国产清高在天天线| 亚洲最大成人手机在线| 观看免费一级毛片| 三级男女做爰猛烈吃奶摸视频| 少妇丰满av| 日本a在线网址| 麻豆精品久久久久久蜜桃| 欧美一区二区亚洲| 一级黄片播放器| 波多野结衣巨乳人妻| 国产爱豆传媒在线观看| 丰满乱子伦码专区| 在线看三级毛片| 在线国产一区二区在线| 国产av在哪里看| 中文字幕熟女人妻在线| 简卡轻食公司| 欧美+日韩+精品| 亚洲成人精品中文字幕电影| 一个人观看的视频www高清免费观看| 老司机福利观看| 亚洲最大成人中文| 中文字幕av成人在线电影| 99久久久亚洲精品蜜臀av| 免费观看人在逋| 熟妇人妻久久中文字幕3abv| 97人妻精品一区二区三区麻豆| 欧美一区二区亚洲| 特大巨黑吊av在线直播| 伦精品一区二区三区| 少妇人妻一区二区三区视频| 欧美成人a在线观看| 亚洲第一电影网av| 一级黄色大片毛片| 亚洲 国产 在线| av在线亚洲专区| 欧美日本亚洲视频在线播放| 亚洲黑人精品在线| 欧美国产日韩亚洲一区| 搡老熟女国产l中国老女人| 国语自产精品视频在线第100页| 久久国产精品人妻蜜桃| 日本欧美国产在线视频| 日韩大尺度精品在线看网址| 2021天堂中文幕一二区在线观| 少妇裸体淫交视频免费看高清| 亚洲欧美精品综合久久99| 色综合色国产| 国产精品一区二区三区四区久久| 国产亚洲欧美98| 国产精品乱码一区二三区的特点| 精品乱码久久久久久99久播| 最近在线观看免费完整版| 精品久久久久久久人妻蜜臀av| 神马国产精品三级电影在线观看| 欧美黑人巨大hd| 99久久成人亚洲精品观看| av.在线天堂| 天堂√8在线中文| 国产成人av教育| 91狼人影院| 日韩中字成人| 麻豆国产av国片精品| 人人妻人人看人人澡| 色在线成人网| 在线观看午夜福利视频| 大又大粗又爽又黄少妇毛片口| 成人毛片a级毛片在线播放| 亚洲av日韩精品久久久久久密| www.www免费av| 亚洲精品456在线播放app | 他把我摸到了高潮在线观看| 真人一进一出gif抽搐免费| 成年免费大片在线观看| 两性午夜刺激爽爽歪歪视频在线观看| 国产免费一级a男人的天堂| 久久久久久久久大av| 久久久色成人| 91狼人影院| 日韩精品有码人妻一区| 在线观看午夜福利视频| 久久精品91蜜桃| 麻豆成人午夜福利视频| 亚洲成av人片在线播放无| 亚洲av成人精品一区久久| a级一级毛片免费在线观看| 国产精品一区二区性色av| 欧美日韩中文字幕国产精品一区二区三区| 日本黄色片子视频| 黄色日韩在线| a级毛片a级免费在线| 免费看av在线观看网站| 欧美精品啪啪一区二区三区| 亚州av有码| bbb黄色大片| 国产探花极品一区二区| 黄色女人牲交| 韩国av在线不卡| 成人高潮视频无遮挡免费网站| 婷婷六月久久综合丁香| 简卡轻食公司| 欧美绝顶高潮抽搐喷水| 免费av毛片视频| av女优亚洲男人天堂| 亚洲国产日韩欧美精品在线观看| 国产精品,欧美在线| 国产成人aa在线观看| 久久久久久久久久成人| 国产精品国产三级国产av玫瑰| 一进一出抽搐动态| 伦理电影大哥的女人| 亚洲av美国av| 欧美色欧美亚洲另类二区| 少妇高潮的动态图| 长腿黑丝高跟| 欧美极品一区二区三区四区| 欧美一区二区精品小视频在线| 免费观看人在逋| av黄色大香蕉| 国产精品福利在线免费观看| 禁无遮挡网站| 亚洲国产精品合色在线| 亚洲国产欧洲综合997久久,| 亚洲一区高清亚洲精品| 亚洲人成网站在线播放欧美日韩| 最近视频中文字幕2019在线8| 91麻豆av在线| 日本黄大片高清| 乱人视频在线观看| 内地一区二区视频在线| 日本免费一区二区三区高清不卡| 嫩草影院入口| av在线亚洲专区| 日日撸夜夜添| 成人二区视频| 国产女主播在线喷水免费视频网站 | 99视频精品全部免费 在线| 国产一区二区在线av高清观看| 久久精品国产99精品国产亚洲性色| 三级男女做爰猛烈吃奶摸视频| 丰满乱子伦码专区| 久久精品国产亚洲av天美| 12—13女人毛片做爰片一| 亚洲av第一区精品v没综合| 一本精品99久久精品77| 免费看a级黄色片| 97热精品久久久久久| 免费一级毛片在线播放高清视频| 午夜a级毛片| 乱系列少妇在线播放| 日本熟妇午夜| 欧美黑人欧美精品刺激| 中出人妻视频一区二区| 在线天堂最新版资源| 俄罗斯特黄特色一大片| 男女边吃奶边做爰视频| 色视频www国产| 亚洲国产高清在线一区二区三| 国产精品女同一区二区软件 | 麻豆国产97在线/欧美| 国产精品伦人一区二区| 人妻夜夜爽99麻豆av| 国产高清有码在线观看视频| 久久久久久久久中文| 国产高清激情床上av| 美女cb高潮喷水在线观看| 亚洲无线观看免费| 亚州av有码| 中出人妻视频一区二区| 日韩人妻高清精品专区| videossex国产| 18+在线观看网站| 国产精品久久久久久精品电影| 午夜激情欧美在线| 夜夜看夜夜爽夜夜摸| 制服丝袜大香蕉在线| 日本一本二区三区精品| 在线观看一区二区三区| 午夜激情欧美在线| 国产视频一区二区在线看| 偷拍熟女少妇极品色| 久久人妻av系列| 精品久久久久久,| 在现免费观看毛片| 亚洲va日本ⅴa欧美va伊人久久| 哪里可以看免费的av片| 女的被弄到高潮叫床怎么办 | 色视频www国产| 精品一区二区三区视频在线观看免费| 欧美激情在线99| 国内精品久久久久精免费| 国产午夜福利久久久久久| 国产高清视频在线观看网站| 三级毛片av免费| 午夜视频国产福利| 国产精品久久久久久亚洲av鲁大| 美女xxoo啪啪120秒动态图| 韩国av在线不卡| 亚洲国产日韩欧美精品在线观看| 3wmmmm亚洲av在线观看| 欧美在线一区亚洲| 亚洲第一电影网av| 亚洲第一区二区三区不卡| 日韩欧美三级三区| 桃红色精品国产亚洲av| 国产激情偷乱视频一区二区| 自拍偷自拍亚洲精品老妇| 亚洲av一区综合| 婷婷丁香在线五月| av福利片在线观看| 深夜精品福利| 韩国av在线不卡| 在线观看舔阴道视频| 亚洲美女黄片视频| 久久久久久久精品吃奶| 中文在线观看免费www的网站| 国产高潮美女av| 免费搜索国产男女视频| 特级一级黄色大片| or卡值多少钱| 国产av麻豆久久久久久久| 亚洲综合色惰| 日本三级黄在线观看| 午夜福利18| 久久久国产成人免费| 免费av不卡在线播放| 校园人妻丝袜中文字幕| 欧美高清成人免费视频www| 国产男人的电影天堂91| 精品日产1卡2卡| 久久久久久九九精品二区国产| 高清毛片免费观看视频网站| 一级黄色大片毛片| 夜夜爽天天搞| 伦理电影大哥的女人| 欧美一区二区亚洲| 亚洲午夜理论影院| 国产一区二区亚洲精品在线观看| 啦啦啦观看免费观看视频高清| 婷婷六月久久综合丁香| 欧美另类亚洲清纯唯美| 国产精品无大码| 在线免费观看不下载黄p国产 | 51国产日韩欧美| 亚洲国产高清在线一区二区三| 啪啪无遮挡十八禁网站| 日韩,欧美,国产一区二区三区 | 亚洲国产精品合色在线| 校园人妻丝袜中文字幕| 欧美人与善性xxx| 九九热线精品视视频播放| 成人综合一区亚洲| 深夜精品福利| 精品一区二区三区av网在线观看| 亚洲自偷自拍三级| 国产大屁股一区二区在线视频| www日本黄色视频网| 麻豆精品久久久久久蜜桃| ponron亚洲| 成年人黄色毛片网站| 在线观看66精品国产| 色播亚洲综合网| 国产午夜精品论理片| 噜噜噜噜噜久久久久久91| 国产av麻豆久久久久久久| 波多野结衣高清作品| 天堂影院成人在线观看| 日韩欧美一区二区三区在线观看| 亚洲图色成人| 精品一区二区免费观看| 亚洲不卡免费看| 一a级毛片在线观看| 亚洲色图av天堂| 校园人妻丝袜中文字幕| 亚洲精华国产精华液的使用体验 | 免费av毛片视频| 蜜桃久久精品国产亚洲av| 欧美日韩精品成人综合77777| 免费看av在线观看网站| 少妇人妻一区二区三区视频| 97超级碰碰碰精品色视频在线观看| 日韩人妻高清精品专区| 亚洲人与动物交配视频| 亚洲精品一卡2卡三卡4卡5卡| 亚洲国产欧美人成| 直男gayav资源| 午夜福利高清视频| 久久亚洲真实| 搡老熟女国产l中国老女人| 黄色女人牲交| 欧美丝袜亚洲另类 | 69人妻影院| 国产大屁股一区二区在线视频| 日韩精品青青久久久久久| 91久久精品国产一区二区成人| 久久国产精品人妻蜜桃| 国产真实伦视频高清在线观看 | 99视频精品全部免费 在线| 欧美日韩中文字幕国产精品一区二区三区| 亚洲av熟女| 久久久久久伊人网av| 精品日产1卡2卡| 日韩中字成人| 成人亚洲精品av一区二区| 免费av不卡在线播放| 麻豆精品久久久久久蜜桃| 伊人久久精品亚洲午夜| 国产91精品成人一区二区三区| 日本欧美国产在线视频| 亚洲无线观看免费| 亚洲成人中文字幕在线播放| 国产人妻一区二区三区在| 欧美激情久久久久久爽电影| 深夜精品福利| 国产单亲对白刺激| 麻豆成人av在线观看| 丰满乱子伦码专区| 直男gayav资源| 男人舔奶头视频| 亚洲五月天丁香| 精品久久久久久久久久免费视频| 久久久午夜欧美精品| 在线观看午夜福利视频| 欧美人与善性xxx| 亚洲内射少妇av| 99久久成人亚洲精品观看| 亚洲 国产 在线| 一区二区三区免费毛片| 在线播放无遮挡| 亚洲av免费在线观看| 两人在一起打扑克的视频| 日韩中文字幕欧美一区二区| 综合色av麻豆| 久久久久久久久久久丰满 | 精品一区二区三区视频在线观看免费| 五月玫瑰六月丁香| www.色视频.com| 夜夜爽天天搞| 黄色丝袜av网址大全| 伦理电影大哥的女人| 精华霜和精华液先用哪个| 日日干狠狠操夜夜爽| 亚洲欧美激情综合另类| 国产精品野战在线观看| 亚洲中文字幕日韩| 黄色女人牲交| 免费搜索国产男女视频| 国产成人影院久久av| 88av欧美| 97热精品久久久久久| 国产av一区在线观看免费| 网址你懂的国产日韩在线| 色噜噜av男人的天堂激情| 欧美zozozo另类| 国产又黄又爽又无遮挡在线| 国产精品久久久久久久电影| 国产91精品成人一区二区三区| 亚洲av免费高清在线观看| 女人被狂操c到高潮| a级一级毛片免费在线观看| 午夜福利18| 毛片女人毛片| 老女人水多毛片| 人人妻,人人澡人人爽秒播| 久久久久九九精品影院| 国产探花极品一区二区| 国产精品三级大全| 欧美日韩亚洲国产一区二区在线观看| 一区二区三区高清视频在线| 成人无遮挡网站| 两性午夜刺激爽爽歪歪视频在线观看| 亚洲av美国av| 老司机福利观看| 亚洲中文字幕一区二区三区有码在线看| 亚洲七黄色美女视频| 免费观看精品视频网站| 丰满的人妻完整版| 久久久久久久亚洲中文字幕| 亚洲av日韩精品久久久久久密| 在线播放国产精品三级| 国产伦精品一区二区三区视频9| 真实男女啪啪啪动态图| 国产精品日韩av在线免费观看| 欧美日本视频| 天天躁日日操中文字幕| 午夜福利在线观看免费完整高清在 | 久久国内精品自在自线图片| 美女cb高潮喷水在线观看| 成人永久免费在线观看视频| 国产高清视频在线观看网站| 精品99又大又爽又粗少妇毛片 | 在线观看美女被高潮喷水网站| 亚洲三级黄色毛片| 亚洲真实伦在线观看| 国产亚洲av嫩草精品影院| 欧美绝顶高潮抽搐喷水| 国产一区二区三区在线臀色熟女| 99热这里只有是精品50| 国产高清激情床上av| 老司机午夜福利在线观看视频| 男人舔奶头视频| 国产精品一区www在线观看 | 亚洲不卡免费看| 日本精品一区二区三区蜜桃| 久久久久免费精品人妻一区二区| 色播亚洲综合网| 亚洲中文字幕一区二区三区有码在线看| 热99re8久久精品国产| www日本黄色视频网| 国产色爽女视频免费观看| 久久久久久大精品| 婷婷亚洲欧美| 麻豆成人午夜福利视频| 97人妻精品一区二区三区麻豆| 99久久成人亚洲精品观看| 国产成人福利小说| 天天一区二区日本电影三级| 春色校园在线视频观看| 亚洲精品在线观看二区| 久久久久久久久久久丰满 | 国产精品永久免费网站| 亚洲精品粉嫩美女一区| 看免费成人av毛片| 好男人在线观看高清免费视频| 亚洲真实伦在线观看| 久久精品国产亚洲av天美| 亚洲熟妇熟女久久| 熟妇人妻久久中文字幕3abv| 午夜免费激情av| 久久久午夜欧美精品| 欧美高清性xxxxhd video| 精品午夜福利在线看| 尾随美女入室| a在线观看视频网站| 97碰自拍视频| 色尼玛亚洲综合影院| 精品久久国产蜜桃| 搡老熟女国产l中国老女人| 少妇裸体淫交视频免费看高清| 国产午夜精品论理片| 国产精品女同一区二区软件 | 亚洲在线观看片| 久久久久久伊人网av| 久久久精品大字幕| 天堂√8在线中文| 小蜜桃在线观看免费完整版高清| 久久精品综合一区二区三区| 亚洲午夜理论影院| 亚洲av一区综合| 日韩精品中文字幕看吧| videossex国产| 久久香蕉精品热| 性色avwww在线观看| 黄色配什么色好看| 亚洲精华国产精华精| .国产精品久久| 久久亚洲真实| 亚洲人成网站在线播放欧美日韩| 高清毛片免费观看视频网站| 精品一区二区三区人妻视频| 国内精品宾馆在线| 国产一区二区三区视频了| 99久久无色码亚洲精品果冻| 国产午夜精品论理片| 久久久精品欧美日韩精品| 日日摸夜夜添夜夜添av毛片 | 窝窝影院91人妻| 国产一区二区亚洲精品在线观看| 日日摸夜夜添夜夜添小说| 色哟哟·www| 成人欧美大片| 色哟哟·www| 18+在线观看网站| 免费观看人在逋| 精品福利观看| 日韩高清综合在线| 亚洲电影在线观看av| 国产亚洲av嫩草精品影院| 动漫黄色视频在线观看| 精品欧美国产一区二区三| 两个人的视频大全免费| 午夜激情福利司机影院| 嫩草影视91久久| 麻豆av噜噜一区二区三区| 村上凉子中文字幕在线| 亚洲欧美精品综合久久99| 3wmmmm亚洲av在线观看| 很黄的视频免费| 男人舔奶头视频| 非洲黑人性xxxx精品又粗又长| 人人妻,人人澡人人爽秒播| 亚洲欧美激情综合另类| 亚洲自拍偷在线| 欧美极品一区二区三区四区| 久久精品国产亚洲av香蕉五月| 久久久久久久久久久丰满 | 日本欧美国产在线视频| 婷婷精品国产亚洲av在线| 亚洲av不卡在线观看| 久久中文看片网| 免费在线观看日本一区| 舔av片在线| 亚洲色图av天堂| 男女下面进入的视频免费午夜| 日本一本二区三区精品| 久久久久久大精品| 亚洲国产精品合色在线| 国产成人影院久久av| 中文字幕av成人在线电影| 亚洲一区高清亚洲精品| 一a级毛片在线观看| 欧美成人免费av一区二区三区| 国产精品久久久久久精品电影| 大又大粗又爽又黄少妇毛片口| 免费看美女性在线毛片视频| av福利片在线观看| 能在线免费观看的黄片| 久久人人精品亚洲av| 尤物成人国产欧美一区二区三区| 久久精品国产亚洲av香蕉五月| 久久久精品大字幕| 亚洲狠狠婷婷综合久久图片| 国产精品乱码一区二三区的特点| videossex国产| 亚洲一区二区三区色噜噜| 国内精品久久久久久久电影| av国产免费在线观看| 天堂影院成人在线观看| 琪琪午夜伦伦电影理论片6080|