自从Zabusky和kruskal对方程(1)的周期初值问题作出历史性的数值实验后,人们对kdv方程的纯初值问题得到许多理论上的进展,如逆散射技巧、Bclund变换、painleve性质、广义Hamilton结构等等;在数值计算上也作了大量工作。但是对于有更强...自从Zabusky和kruskal对方程(1)的周期初值问题作出历史性的数值实验后,人们对kdv方程的纯初值问题得到许多理论上的进展,如逆散射技巧、Bclund变换、painleve性质、广义Hamilton结构等等;在数值计算上也作了大量工作。但是对于有更强实际背景的初边值问题,却未引起足够重视。Bui An Ton在齐次边界条件f(t)展开更多
The Lax pair of the mixed Ablowitz-Kap-Newell-Segur （AKNS） system is obtained from compatibility condition. Hirota＇s bilinear form is derived by some dependent variable transformation. Moreover, by means of the Wro...The Lax pair of the mixed Ablowitz-Kap-Newell-Segur （AKNS） system is obtained from compatibility condition. Hirota＇s bilinear form is derived by some dependent variable transformation. Moreover, by means of the Wronskian technique, the double Wronskian form of soliton solutions are found. Specially, the two-soliton solution is presented.展开更多
Solutions in the Crammian form for a non-isospectral Kadomtsev-Petviashvili equation are derived by means of Pfaffian derivative formulae. Explicit entries of the Crammian are given. Non-isospectral dynamics of the so...Solutions in the Crammian form for a non-isospectral Kadomtsev-Petviashvili equation are derived by means of Pfaffian derivative formulae. Explicit entries of the Crammian are given. Non-isospectral dynamics of the solutions generated from the Crammian are investigated in an analytic way. The solutions obtained can describe line solitons in non-uniform media travelling with time-dependent amplitude and time-dependent direction. In addition, some other solutions have singularities.展开更多
The bilinear form for a nonisospectral and variable-coefficient Kadomtsev-Petviashvili equation is obtained and some exact soliton solutions are derived by the Hirota method and Wronskian technique. We also derive the...The bilinear form for a nonisospectral and variable-coefficient Kadomtsev-Petviashvili equation is obtained and some exact soliton solutions are derived by the Hirota method and Wronskian technique. We also derive the bilinear Backlund transformation from its Lax pairs and find solutions with the help of the obtained bilinear Bgcklund transformation.展开更多
A new explicit scheme for the Korteweg~：le Vries （KdV） equation is proposed. The scheme is more stable than the Zabusky Kruskal scheme and the multi-symplectic six-point scheme. When used to simulate the collisions...A new explicit scheme for the Korteweg~：le Vries （KdV） equation is proposed. The scheme is more stable than the Zabusky Kruskal scheme and the multi-symplectic six-point scheme. When used to simulate the collisions of multi-soliton, it does not show the nonlinear instabilities and un-physical oscillations.展开更多
Two-dimensional （219） relativistic magnetosonic solitons in the negative-ion-rich plasma consisting of positive ions Ar＋, negative ions SF6 and electrons are investigated in the presence of an applied magnetic fiel...Two-dimensional （219） relativistic magnetosonic solitons in the negative-ion-rich plasma consisting of positive ions Ar＋, negative ions SF6 and electrons are investigated in the presence of an applied magnetic field Bo and can be described by a Kadomtse-Petviashvili （KP） equation in the weakly relativistic limit. The ratio of positive ion density to negative ion density has a marked influence on the amplitude φm and width W of the steady-state KP soliton. The interaction law of the nontrivial solitons with rich web structure is studied by the Wronskian determinant method.展开更多
By using a weakly nonlinear and perturbation method, the generalized inhomogeneous Korteweg de Vries （KdV）- Burgers equation is derived, which governs the evolution of the amplitude of Rossby waves under the influen...By using a weakly nonlinear and perturbation method, the generalized inhomogeneous Korteweg de Vries （KdV）- Burgers equation is derived, which governs the evolution of the amplitude of Rossby waves under the influence of dissipation and slowly varying topography with time. The analysis indicates that dissipation and slowly varying topography with time are important factors in causing variation in the mass and energy of solitary waves.展开更多
文摘自从Zabusky和kruskal对方程(1)的周期初值问题作出历史性的数值实验后,人们对kdv方程的纯初值问题得到许多理论上的进展,如逆散射技巧、Bclund变换、painleve性质、广义Hamilton结构等等;在数值计算上也作了大量工作。但是对于有更强实际背景的初边值问题,却未引起足够重视。Bui An Ton在齐次边界条件f(t)
基金Supported by the National Natural Science Foundation of China under Grant No 10371070.
文摘The Lax pair of the mixed Ablowitz-Kap-Newell-Segur （AKNS） system is obtained from compatibility condition. Hirota＇s bilinear form is derived by some dependent variable transformation. Moreover, by means of the Wronskian technique, the double Wronskian form of soliton solutions are found. Specially, the two-soliton solution is presented.
基金Supported by the National Natural Science Foundation of China under Grant No10371070, and the Foundation of Shanghai Education Committee for Shanghai Prospective Excellent Young Teachers.
文摘Solutions in the Crammian form for a non-isospectral Kadomtsev-Petviashvili equation are derived by means of Pfaffian derivative formulae. Explicit entries of the Crammian are given. Non-isospectral dynamics of the solutions generated from the Crammian are investigated in an analytic way. The solutions obtained can describe line solitons in non-uniform media travelling with time-dependent amplitude and time-dependent direction. In addition, some other solutions have singularities.
基金Supported by the National Natural Science Foundation of China under Grant No 10371070, and the Postdoctoral Science Foundation of China.
文摘The bilinear form for a nonisospectral and variable-coefficient Kadomtsev-Petviashvili equation is obtained and some exact soliton solutions are derived by the Hirota method and Wronskian technique. We also derive the bilinear Backlund transformation from its Lax pairs and find solutions with the help of the obtained bilinear Bgcklund transformation.
基金Supported by the National Basic Research Programme of China under Grant No 2005CB321703, the National Natural Science Foundation of China under Grant Nos 10471067 and 40405019, and the Key Project of Jiangsu NSF （BK2006725）.
文摘A new explicit scheme for the Korteweg~：le Vries （KdV） equation is proposed. The scheme is more stable than the Zabusky Kruskal scheme and the multi-symplectic six-point scheme. When used to simulate the collisions of multi-soliton, it does not show the nonlinear instabilities and un-physical oscillations.
基金Supported by the National Natural Science Foundation of China under Grant No 10747109, and the Research Fund for the Doctoral Programme of Higher Education of China under Grant No 20070008001.
文摘Two-dimensional （219） relativistic magnetosonic solitons in the negative-ion-rich plasma consisting of positive ions Ar＋, negative ions SF6 and electrons are investigated in the presence of an applied magnetic field Bo and can be described by a Kadomtse-Petviashvili （KP） equation in the weakly relativistic limit. The ratio of positive ion density to negative ion density has a marked influence on the amplitude φm and width W of the steady-state KP soliton. The interaction law of the nontrivial solitons with rich web structure is studied by the Wronskian determinant method.
基金supported by the Knowledge Innovation Key Program of the Chinese Academy of Sciences (Grant No. KZCX1-YW-12)the National Key Science Foundation of China (Grant No. 41030855)
文摘By using a weakly nonlinear and perturbation method, the generalized inhomogeneous Korteweg de Vries （KdV）- Burgers equation is derived, which governs the evolution of the amplitude of Rossby waves under the influence of dissipation and slowly varying topography with time. The analysis indicates that dissipation and slowly varying topography with time are important factors in causing variation in the mass and energy of solitary waves.
