广义Kadomtsev-Petviashvili方程的一些精确解

IF 1 4区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Advances in Mathematical Physics Pub Date : 2022-11-28 DOI:10.1155/2022/9882817

Bao Wang, Zhiqiang Chen

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引用次数: 0

摘要

大多数论文都探讨了零背景孤子之间的相互作用，而关于非零背景孤子的精确解的报道很少。因此，本文旨在探讨(2 + 1)维广义Kadomtsev-Petviashvili (gKP)方程的呼吸解、块解和具有小扰动的相互作用解。利用Hirota的双线性方法得到了具有小扰动的一般高阶周期呼吸解。同时，结合使用长波极限法和模共振约束，得到了gKP方程的一般整体解和混合解。最后，对呼吸解、块解和相互作用解的时空结构进行了研究和讨论。

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Some Exact Solutions to Generalized Kadomtsev-Petviashvili Equation

Most of the papers have explored the interactions between solitons with a zero background, while reports about exact solutions for nonzero background are rare. Hence, this paper is aimed at exploring the breather, lump, and interaction solutions with a small perturbation to ( 2 + 1 )-dimensional generalized Kadomtsev-Petviashvili (gKP) equation. General high-order periodic breather solutions are obtained using Hirota’s bilinear method with a small perturbation. At the same time, combining the use of long wave limit methods and module resonance constraints, general lump solutions and mixed solutions to gKP equation are generated. Finally, the space-time structures of the breather solutions, lump solutions, and interaction solutions are investigated and discussed.

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来源期刊

Advances in Mathematical Physics 数学-应用数学

CiteScore

2.40

自引率

8.30%

发文量

151

审稿时长

>12 weeks

期刊介绍： Advances in Mathematical Physics publishes papers that seek to understand mathematical basis of physical phenomena, and solve problems in physics via mathematical approaches. The journal welcomes submissions from mathematical physicists, theoretical physicists, and mathematicians alike. As well as original research, Advances in Mathematical Physics also publishes focused review articles that examine the state of the art, identify emerging trends, and suggest future directions for developing fields.