The present paper proposes a Lagrangian criterion of unsteady flow separation for two-dimensional periodic flows based on the principle of weighted averaging zero skin-friction given by Haller （HALLER, G. Exact theor...The present paper proposes a Lagrangian criterion of unsteady flow separation for two-dimensional periodic flows based on the principle of weighted averaging zero skin-friction given by Haller （HALLER, G. Exact theory of unsteady separation for two-dimensional flows. Journal of Fluid Mechanics, 512, 257-311 （2004））. By analyzing the distribution of the finite-time Lyapunov exponent （FTLE） along the no-slip wall, it can be found that the periodic separation takes place at the point of the zero FTLE. This new criterion is verified with an analytical solution of the separation bubble and a numerical simulation of lid-driven cavity flows.展开更多
By means of the standard truncated Painlevé expansion and a variable separation approach, a general variable separation solution of the generalized Burgers system is derived. In addition to the usual localized co...By means of the standard truncated Painlevé expansion and a variable separation approach, a general variable separation solution of the generalized Burgers system is derived. In addition to the usual localized coherent soliton excitations like dromions, lumps, rings, breathers, instantons, oscillating soliton excitations, peakons, foldons,and previously revealed chaotic and fractal localized solutions, some new types of excitations compacton and dacobi periodic wave solutions are obtained by introducing appropriate lower dimensional piecewise smooth functions and Jacobi elliptic functions.展开更多
The linear variable separation approach is successfully extended to (1+1)-dimensional Korteweg-de Vries (KdV) type models related to Schrǒdinger system. Some significant types of solitons such as compacton, peakon, a...The linear variable separation approach is successfully extended to (1+1)-dimensional Korteweg-de Vries (KdV) type models related to Schrǒdinger system. Some significant types of solitons such as compacton, peakon, and loop solutions with periodic behavior are simultaneously derived from the (1+1)-dimensional soliton system by entrancing appropriate piecewise smooth functions and multivalued functions.展开更多
By introducing the Lucas-Riccati method and a linear variable separation method,new variable separationsolutions with arbitrary functions are derived for a(2+1)-dimensional modified dispersive water-wave system.The ma...By introducing the Lucas-Riccati method and a linear variable separation method,new variable separationsolutions with arbitrary functions are derived for a(2+1)-dimensional modified dispersive water-wave system.The mainidea of this method is to express the solutions of this system as polynomials in the solution of the Riccati equation thatthe symmetrical Lucas functions satisfy.From the variable separation solution and by selecting appropriate functions,some novel Jacobian elliptic wave structure with variable modulus and their interactions with dromions and peakons areinvestigated.展开更多
In the paper, the variable separation approach, homoclinic test technique and bilinear method are successfullyextended to a (1+1)-dimensional Caudry-Dodd-Gibbon-Sawada-Kortera (CDGSK) system, respectively.Basedon the ...In the paper, the variable separation approach, homoclinic test technique and bilinear method are successfullyextended to a (1+1)-dimensional Caudry-Dodd-Gibbon-Sawada-Kortera (CDGSK) system, respectively.Basedon the derived exact solutions, some significant types of localized excitations such as standing waves, periodic waves,solitary waves are simultaneously derived from the (1+1)-dimensional Caudry-Dodd-Gibbon-Sawada-Kortera systemby entrancing appropriate parameters.展开更多
基金supported by the National Natural Science Foundation of China(Nos.11372340 and 11732016)
文摘The present paper proposes a Lagrangian criterion of unsteady flow separation for two-dimensional periodic flows based on the principle of weighted averaging zero skin-friction given by Haller （HALLER, G. Exact theory of unsteady separation for two-dimensional flows. Journal of Fluid Mechanics, 512, 257-311 （2004））. By analyzing the distribution of the finite-time Lyapunov exponent （FTLE） along the no-slip wall, it can be found that the periodic separation takes place at the point of the zero FTLE. This new criterion is verified with an analytical solution of the separation bubble and a numerical simulation of lid-driven cavity flows.
基金The project supported by National Natural Science Foundation of China under Grant No.10172056+2 种基金
the Natural Science Foundation of Zhengjiang Province
the Foundation of Zhengjiang Lishui College under Grant Nos.KZ03009 and KZ03005
文摘By means of the standard truncated Painlevé expansion and a variable separation approach, a general variable separation solution of the generalized Burgers system is derived. In addition to the usual localized coherent soliton excitations like dromions, lumps, rings, breathers, instantons, oscillating soliton excitations, peakons, foldons,and previously revealed chaotic and fractal localized solutions, some new types of excitations compacton and dacobi periodic wave solutions are obtained by introducing appropriate lower dimensional piecewise smooth functions and Jacobi elliptic functions.
基金The project supported by National Natural Science Foundation of China under Grant No. 10172056, and the Natural Science Foundation of Zhejiang Province of China under Grant No. Y604106 and the Natural Science Foundation of Zhejiang Lishui University unde
文摘The linear variable separation approach is successfully extended to (1+1)-dimensional Korteweg-de Vries (KdV) type models related to Schrǒdinger system. Some significant types of solitons such as compacton, peakon, and loop solutions with periodic behavior are simultaneously derived from the (1+1)-dimensional soliton system by entrancing appropriate piecewise smooth functions and multivalued functions.
基金The project supported by National Natural Science Foundation of China under Grant Nos. 90203001 and 10475055 Acknowledgment The authors are indebt to the discussions with Dr H.C. Hu
基金The project supported by the National Natural Science Foundation of China under Grant No. 10272071, the Natural Science Foundation of Zhejiang Province of China under Grant No. Y504111, and the Science Research Foundation of Huzhou University
基金National Natural Science Foundation of China under Grant No.10272071the Natural Science Foundation of Zhejiang Province under Grant No.Y504111the Scientific Research Foundation of Huzhou University
文摘用可变分离途径，我们与任意的可变分离函数获得一个一般准确解决方案为(2+1 ) 维的碎 soliton 系统。由介绍 Jacobi 在种子答案的椭圆形的功能，二倍地周期的宣传的二个家庭挥动模式被导出。我们与不同模量 m 选择调查这些周期的波浪答案，许多重要、有趣的性质被揭示。Jabcobi 椭圆形的功能波浪的相互作用图形地被考虑并且发现了无弹性。
文摘By introducing the Lucas-Riccati method and a linear variable separation method,new variable separationsolutions with arbitrary functions are derived for a(2+1)-dimensional modified dispersive water-wave system.The mainidea of this method is to express the solutions of this system as polynomials in the solution of the Riccati equation thatthe symmetrical Lucas functions satisfy.From the variable separation solution and by selecting appropriate functions,some novel Jacobian elliptic wave structure with variable modulus and their interactions with dromions and peakons areinvestigated.
基金Supported the Natural Science Foundation of Guangdong Province of China under Grant No.10151200501000008 the Special Foundation of Talent Engineering of Guangdong Province+2 种基金the Scientific Research Foundation of Key Discipline of Guangdong Shaoguan University under Grant No.KZ2009001the Natural Science Foundation of Zhejiang Province of China under Grant Nos.Y604106 and Y606181the Foundation of New Century "151 Talent Engineering" of Zhejiang Province
文摘In the paper, the variable separation approach, homoclinic test technique and bilinear method are successfullyextended to a (1+1)-dimensional Caudry-Dodd-Gibbon-Sawada-Kortera (CDGSK) system, respectively.Basedon the derived exact solutions, some significant types of localized excitations such as standing waves, periodic waves,solitary waves are simultaneously derived from the (1+1)-dimensional Caudry-Dodd-Gibbon-Sawada-Kortera systemby entrancing appropriate parameters.
基金Foundation item： Supported by the National Natural Science Foundation of China（10647112, 10871040） Acknowledgement The authors are in debt to thank the helpful discussions with Prof Qin and Dr A P Deng.
