A novel (2+1)-dimensional integrable KdV equation with peculiar solution structures

doi:10.1088/1674-1056/ab9699

中国物理B ›› 2020, Vol. 29 ›› Issue (8): 80502-080502.doi: 10.1088/1674-1056/ab9699

• SPECIAL TOPIC—Ultracold atom and its application in precision measurement • 上一篇下一篇

A novel (2+1)-dimensional integrable KdV equation with peculiar solution structures

Sen-Yue Lou(楼森岳)

School of Physical Science and Technology, Ningbo University, Ningbo 315211, China

收稿日期:2020-04-06 修回日期:2020-05-19 出版日期:2020-08-05 发布日期:2020-08-05
通讯作者: Sen-Yue Lou E-mail:lousenyue@nbu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11975131 and 11435005) and K. C. Wong Magna Fund in Ningbo University.

A novel (2+1)-dimensional integrable KdV equation with peculiar solution structures

Sen-Yue Lou(楼森岳)

School of Physical Science and Technology, Ningbo University, Ningbo 315211, China

Received:2020-04-06 Revised:2020-05-19 Online:2020-08-05 Published:2020-08-05
Contact: Sen-Yue Lou E-mail:lousenyue@nbu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11975131 and 11435005) and K. C. Wong Magna Fund in Ningbo University.

摘要/Abstract

摘要：

The celebrated (1+1)-dimensional Korteweg de-Vries (KdV) equation and its (2+1)-dimensional extension, the Kadomtsev-Petviashvili (KP) equation, are two of the most important models in physical science. The KP hierarchy is explicitly written out by means of the linearized operator of the KP equation. A novel (2+1)-dimensional KdV extension, the cKP3-4 equation, is obtained by combining the third member (KP3, the usual KP equation) and the fourth member (KP4) of the KP hierarchy. The integrability of the cKP3-4 equation is guaranteed by the existence of the Lax pair and dual Lax pair. The cKP3-4 system can be bilinearized by using Hirota's bilinear operators after introducing an additional auxiliary variable. Exact solutions of the cKP3-4 equation possess some peculiar and interesting properties which are not valid for the KP3 and KP4 equations. For instance, the soliton molecules and the missing D'Alembert type solutions (the arbitrary travelling waves moving in one direction with a fixed model dependent velocity) including periodic kink molecules, periodic kink-antikink molecules, few-cycle solitons, and envelope solitons exist for the cKP3-4 equation but not for the separated KP3 equation and the KP4 equation.

关键词: (2+1)-dimensional KdV equations, Lax and dual Lax pairs, soliton and soliton molecules, D'Alembert type waves

Abstract:

Key words: (2+1)-dimensional KdV equations, Lax and dual Lax pairs, soliton and soliton molecules, D'Alembert type waves

中图分类号: (Solitons)

05.45.Yv

02.30.Ik (Integrable systems) 47.20.Ky (Nonlinearity, bifurcation, and symmetry breaking) 52.35.Mw (Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.))

楼森岳. A novel (2+1)-dimensional integrable KdV equation with peculiar solution structures[J]. 中国物理B, 2020, 29(8): 80502-080502.

Sen-Yue Lou(楼森岳). A novel (2+1)-dimensional integrable KdV equation with peculiar solution structures[J]. Chin. Phys. B, 2020, 29(8): 80502-080502.

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A novel (2+1)-dimensional integrable KdV equation with peculiar solution structures

A novel (2+1)-dimensional integrable KdV equation with peculiar solution structures

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