一类广义色散方程的行波解
A Study on Exact Travelling Wave Solutions of Generalized Dispersive Equations
DOI: 10.12677/AAM.2018.712186, PDF,   
作者: 陈 静：西南科技大学理学院，四川 绵阳
关键词: 广义非线性KdV方程；紧孤子；孤立子；Generalized KdV-Type Equations； Compactons； Solitons
摘要: 本文在降阶法的基础上运用变量代换法研究了一类广义非线性KdV方程的精确解，获得了这个方程具有不同物理结构包括紧孤子、孤立子、孤立波相似解和周期解在内的行波解。对于这类具有正或负n指数的广义KdV方程，方程中各项的系数连同波速一起决定着解的物理结构。
Abstract: The aim of this paper is devoted to the study of physical structures of solutions for generalized nonlinear KdV-type equations in two-dimensional space. The variable replacement method is used to get compactons, solitons, solitary patterns and periodic solutions. Furthermore, we point out that the different exponents and coefficients lead to different results of physical structures for this kind of equations with positive or negative exponents.
文章引用：陈静. 一类广义色散方程的行波解[J]. 应用数学进展, 2018, 7(12): 1593-1599. https://doi.org/10.12677/AAM.2018.712186

参考文献

[1] Li, B., Chen, Y. and Zhang, H.Q. (2003) Exact Travelling Wave Solutions for a Generalized Zakharov-Kuznetsov Equation. Applied Mathematics and Computation, 146, 653-666. [Google Scholar] [CrossRef] 
[2] Rosenau, P. and Hyman, J.M. (1993) Compactons: Solitons with Finite Wavelength. Physical Review Letters, 70, 564-567. [Google Scholar] [CrossRef] 
[3] Wazwaz, A.M. (2001) A Study of Nonlinear Dispersive Equa-tions with Solitary-Wave Solutions Having Compact Support. Mathematics and Computers in Simulation, 56, 269-276. [Google Scholar] [CrossRef] 
[4] Wazwwaz, A.M. (2005) Variants of the Two-Dimensional Boussinesq Equation with Compactons, Solitons, and Periodic Solutions. Computers and Mathematics with Applications, 49, 295-301. [Google Scholar] [CrossRef] 
[5] Wazwwaz, A.M. (2003) A Study on Nonlinear Dispersive Par-tial Differenial Equations of Compact and Nocompact Solutions, and Nocompact Structures. Applied Mathematics and Computation, 135, 399-409. [Google Scholar] [CrossRef] 
[6] Wazwwaz, A.M. (2004) Dinstinct Variants of the KdV Equation with Compact and Nocompact Structures. Applied Mathematics and Computation, 150, 365-377. [Google Scholar] [CrossRef] 
[7] Kivshar, Y. (1994) Compactons in Dispersive Lattices. Nonlinear Coherent Structures in Physics and Biology, 329, 255-258. [Google Scholar] [CrossRef] 
[8] Dinda, P.T. and Remoissenet, M. (1999) Breather Compactons in Nonlinear Klein-Gordon Systems. Physical Review E, 60, 6218-6221. [Google Scholar] [CrossRef] 
[9] Ismail, M.S. and Taha, T. (1998) A Numerical Study of Com-pactons. Mathematics and Computers in Simulation, 47, 519-530.
[10] Rosenau, P. (2000) Compact and Nocompact Dispersive Structures. Physics Letters A, 275, 193-203. [Google Scholar] [CrossRef] 
[11] Adomian, G. (1994) Solving Frontier Problems of Physics: The Decomposition Method. Kluwer Academic Publishers, Boston. [Google Scholar] [CrossRef] 

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