一个(2 + 1)-维KdV方程的lump解与lump-stripe 混合解
Lump Solutions and Mixed Lump-Stripe Solutions of a (2 + 1)-Dimensional KdV Equation
DOI: 10.12677/MP.2021.116017, PDF,    科研立项经费支持
作者: 陶司兴：商丘师范学院数学与统计学院，河南 商丘
关键词: (2 + 1)-维KdV方程；双线性方法；lump解；lump-stripe混合解；(2 + 1)-Dimensional KdV Equation； Bilinear Method； Lump Solution； Lump Stripe Mixed Solution
摘要: 本文通过利用Hirota双线性形式，并借助Maple符号计算，得到了(2 + 1)-维KdV方程的lump解、lump-stripe混合解。通过选取不同的参数，并结合图像研究了这些解的动力学特征，特别是讨论了lump解和stripe解之间的相互作用现象。这些解及其相关的性质将有助于研究(2 + 1)-维KdV方程所描述的物理学现象。
Abstract: In this paper, by using Hirota bilinear form, the lumped solution and lump strip mixed solution of (2 + 1)-dimensional KdV equation are obtained with the help of Maple symbolic calculation in this paper. By choosing different parameters, the dynamic characteristics of these solutions are studied combined with images, especially the interaction between lumps and stripe solutions. These solutions and their related properties will help to study the dynamic characteristics described by physical phenomena of the (2 + 1)-dimensional KdV equation.
文章引用：陶司兴. 一个(2 + 1)-维KdV方程的lump解与lump-stripe 混合解[J]. 现代物理, 2021, 11(6): 179-189. https://doi.org/10.12677/MP.2021.116017

参考文献

[1] Hirota, R. (2004) The Direct Method in Soliton Theory. Cambridge University Press, Cambridge, England‎. [Google Scholar] [CrossRef] 
[2] Zhang, Y.-F., Tam, H. and Zhao, J. (2006) Higher-Dimensional KdV Equations and Their Soliton Solutions. Communications in Theoretical Physics, 45, 411-413. [Google Scholar] [CrossRef] 
[3] 冯滨鲁, 郭婷婷. (2 + 1)维KdV方程的Gramm解及其pfaffian化[J]. 潍坊学院学报, 2008, 8(6): 75-78.
[4] Ma, W.X. (2015) Lump Solutions to the Kadomtsev-Petviashvili Equa-tion. Physics Letters A, 379, 1975-1978. [Google Scholar] [CrossRef] 
[5] Zhao, Z.L., Chen, Y. and Han, B. (2017) Lump Soliton, Mixed Lump Tripe and Periodic Lump Solutions of a (2 + 1)-Dimensional Asymmetrical Nizhnik-Novikov-Veselov Equation. Modern Physics Letters B, 31, 1750157. [Google Scholar] [CrossRef] 
[6] Chen, S.T. and Ma, W.X. (2018) Lump Solutions to a Genera-lized Bogoyavlensky-Konopelchenko Equation. Frontiers of Mathematics in China, 13, 525-534. [Google Scholar] [CrossRef] 
[7] Chen, S.T. and Ma, W.X. (2018) Lump Solutions of a Generalized Calogero-Bogoyavlenskii-Schiff Equation. Computers & Mathematics with Applications, 76, 1680-1685. [Google Scholar] [CrossRef] 
[8] Zhang, Y.F., Ma, W.X. and Yang, J.Y. (2020) A Study on Lump Solutions to a (2 + 1)-Dimensional Completely Generalized Hirota-Satsuma-Ito Equation. Discrete and Conti-nuous Dynamical Systems, Series S, 13, 2941-2948. [Google Scholar] [CrossRef]