Trajectory equation of a lump before and after collision with line, lump, and breather waves for (2+1)-dimensional Kadomtsev-Petviashvili equation

doi:10.1088/1674-1056/ab44a3

中国物理B ›› 2019, Vol. 28 ›› Issue (11): 110201-110201.doi: 10.1088/1674-1056/ab44a3

• GENERAL • 下一篇

Trajectory equation of a lump before and after collision with line, lump, and breather waves for (2+1)-dimensional Kadomtsev-Petviashvili equation

Zhao Zhang(张钊), Xiangyu Yang(杨翔宇), Wentao Li(李文涛), Biao Li(李彪)

School of Mathematics and Statistics, Ningbo University, Ningbo 315211, China

收稿日期:2019-06-05 修回日期:2019-08-21 出版日期:2019-11-05 发布日期:2019-11-05
通讯作者: Biao Li E-mail:libiao@nbu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11775121, 11805106, and 11435005) and K C Wong Magna Fund in Ningbo University, China.

Trajectory equation of a lump before and after collision with line, lump, and breather waves for (2+1)-dimensional Kadomtsev-Petviashvili equation

Zhao Zhang(张钊), Xiangyu Yang(杨翔宇), Wentao Li(李文涛), Biao Li(李彪)

School of Mathematics and Statistics, Ningbo University, Ningbo 315211, China

Received:2019-06-05 Revised:2019-08-21 Online:2019-11-05 Published:2019-11-05
Contact: Biao Li E-mail:libiao@nbu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11775121, 11805106, and 11435005) and K C Wong Magna Fund in Ningbo University, China.

摘要/Abstract

摘要： Based on the hybrid solutions to (2+1)-dimensional Kadomtsev-Petviashvili (KP) equation, the motion trajectory of the solutions to KP equation is further studied. We obtain trajectory equation of a single lump before and after collision with line, lump, and breather waves by approximating solutions of KP equation along some parallel orbits at infinity. We derive the mathematical expression of the phase change before and after the collision of a lump wave. At the same time, we give some collision plots to reveal the obvious phase change. Our method proposed to find the trajectory equation of a lump wave can be applied to other (2+1)-dimensional integrable equations. The results expand the understanding of lump, breather, and hybrid solutions in soliton theory.

关键词: hybrid solutions, trajectory equation, long wave limit, phase

Abstract: Based on the hybrid solutions to (2+1)-dimensional Kadomtsev-Petviashvili (KP) equation, the motion trajectory of the solutions to KP equation is further studied. We obtain trajectory equation of a single lump before and after collision with line, lump, and breather waves by approximating solutions of KP equation along some parallel orbits at infinity. We derive the mathematical expression of the phase change before and after the collision of a lump wave. At the same time, we give some collision plots to reveal the obvious phase change. Our method proposed to find the trajectory equation of a lump wave can be applied to other (2+1)-dimensional integrable equations. The results expand the understanding of lump, breather, and hybrid solutions in soliton theory.

Key words: hybrid solutions, trajectory equation, long wave limit, phase

中图分类号: (Partial differential equations)

02.30.Jr

05.45.Yv (Solitons) 02.30.Ik (Integrable systems)

张钊, 杨翔宇, 李文涛, 李彪. Trajectory equation of a lump before and after collision with line, lump, and breather waves for (2+1)-dimensional Kadomtsev-Petviashvili equation[J]. 中国物理B, 2019, 28(11): 110201-110201.

Zhao Zhang(张钊), Xiangyu Yang(杨翔宇), Wentao Li(李文涛), Biao Li(李彪). Trajectory equation of a lump before and after collision with line, lump, and breather waves for (2+1)-dimensional Kadomtsev-Petviashvili equation[J]. Chin. Phys. B, 2019, 28(11): 110201-110201.

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Trajectory equation of a lump before and after collision with line, lump, and breather waves for (2+1)-dimensional Kadomtsev-Petviashvili equation

Trajectory equation of a lump before and after collision with line, lump, and breather waves for (2+1)-dimensional Kadomtsev-Petviashvili equation

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