借助 Maple 符号计算软件,利用 Riccati 方程（ξ′= a0＋a1ξ＋a2ξ2）展开法和变量分离法,得到了（2＋1）维Korteweg-de Vries方程（KdV）包含q=C1x＋C2y＋C3t＋R（x, y, t）的复合波解。根据得到的孤立波解,构造出KdV方程新颖的复合...借助 Maple 符号计算软件,利用 Riccati 方程（ξ′= a0＋a1ξ＋a2ξ2）展开法和变量分离法,得到了（2＋1）维Korteweg-de Vries方程（KdV）包含q=C1x＋C2y＋C3t＋R（x, y, t）的复合波解。根据得到的孤立波解,构造出KdV方程新颖的复合波裂变和复合波湮灭等局域激发结构。展开更多
The compound KdV-Burgers equation and combined KdV-mKdV equation are real physical models concerning many branches in physics.In this paper,applying the improved trigonometric function method to these equations,rich e...The compound KdV-Burgers equation and combined KdV-mKdV equation are real physical models concerning many branches in physics.In this paper,applying the improved trigonometric function method to these equations,rich explicit and exact travelling wave solutions,which contain solitary-wave solutions,periodic solutions,and combined formal solitary-wave solutions,are obtained.展开更多
Starting from an improved projective method and a linear variable separation approach, new families of variable separation solutions （including solltary wave solutlons, periodic wave solutions and rational function s...Starting from an improved projective method and a linear variable separation approach, new families of variable separation solutions （including solltary wave solutlons, periodic wave solutions and rational function solutions） with arbitrary functions [or the （2＋ 1）-dimensional general/zed Broer-Kaup （GBK） system are derived. Usually, in terms of solitary wave solutions and/or rational function solutions, one can find abundant important localized excitations. However, based on the derived periodic wave solution in this paper, we reveal some complex wave excitations in the （2＋1）-dimensional GBK system, which describe solitons moving on a periodic wave background. Some interesting evolutional properties for these solitary waves propagating on the periodic wave bactground are also briefly discussed.展开更多
In this paper, we discuss conditional stability of solitary-wave solutions in the sense of Liapunov for the generalized compound KdV equation and the generalized compound KdV-Burgers equations. Linear stability of the...In this paper, we discuss conditional stability of solitary-wave solutions in the sense of Liapunov for the generalized compound KdV equation and the generalized compound KdV-Burgers equations. Linear stability of the exact solitary-wave solutions is proved for the above two types of equations when the small disturbance of travelling wave form satisfies some special conditions.展开更多
文摘借助 Maple 符号计算软件,利用 Riccati 方程（ξ′= a0＋a1ξ＋a2ξ2）展开法和变量分离法,得到了（2＋1）维Korteweg-de Vries方程（KdV）包含q=C1x＋C2y＋C3t＋R（x, y, t）的复合波解。根据得到的孤立波解,构造出KdV方程新颖的复合波裂变和复合波湮灭等局域激发结构。
文摘The compound KdV-Burgers equation and combined KdV-mKdV equation are real physical models concerning many branches in physics.In this paper,applying the improved trigonometric function method to these equations,rich explicit and exact travelling wave solutions,which contain solitary-wave solutions,periodic solutions,and combined formal solitary-wave solutions,are obtained.
基金The project supported by the Natural Science Foundation of Zhejiang Province under Grant Nos. Y604106 and Y606181, the Foundation of New Century ＂151 Talent Engineering＂ of Zhejiang Province, the Scientific Research Foundation of Key Discipline of Zhejiang Province, and the Natural Science Foundation of Zhejiang Lishui University under Grant No. KZ05005 Acknowledgments The authors are in debt to Profs. J.P. Fang, H.P. Zhu, and J.F. Zhang, and Drs. Z.Y. Ma and W.H. Huang for their fruitful discussions.
文摘Starting from an improved projective method and a linear variable separation approach, new families of variable separation solutions （including solltary wave solutlons, periodic wave solutions and rational function solutions） with arbitrary functions [or the （2＋ 1）-dimensional general/zed Broer-Kaup （GBK） system are derived. Usually, in terms of solitary wave solutions and/or rational function solutions, one can find abundant important localized excitations. However, based on the derived periodic wave solution in this paper, we reveal some complex wave excitations in the （2＋1）-dimensional GBK system, which describe solitons moving on a periodic wave background. Some interesting evolutional properties for these solitary waves propagating on the periodic wave bactground are also briefly discussed.
基金The project supported by National Natural Science Foundation of China under Grant No. 10371023 and Shanghai Leading Academic Discipline Project under Grant No. T0502）
文摘In this paper, we discuss conditional stability of solitary-wave solutions in the sense of Liapunov for the generalized compound KdV equation and the generalized compound KdV-Burgers equations. Linear stability of the exact solitary-wave solutions is proved for the above two types of equations when the small disturbance of travelling wave form satisfies some special conditions.
