Bilinear Bäcklund Transformation, Fission/Fusion and Periodic Waves of a (3+1)-dimensional Kadomtsev-Petviashvili Equation for the Shallow Water Waves

被引：6

作者：

Feng, Chun-Hui ^{[1
,2
]}

Tian, Bo ^{[1
,2
]}

Gao, Xiao-Tian ^{[1
,2
]}

机构：

[1] Beijing Univ Posts & Telecommun, State Key Lab Informat Photon & Opt Commun, Beijing 100876, Peoples R China

[2] Beijing Univ Posts & Telecommun, Sch Sci, Beijing 100876, Peoples R China

来源：

INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS | 2024年 / 63卷 / 03期

基金：

中国国家自然科学基金;

关键词：

Shallow water waves; (3+1)-dimensional Kadomtsev-Petviashvili equation; Hirota method; Bilinear Backlund transformation; Fission/Fusion solutions; Periodic-wave solutions; Symbolic computation; OPTICAL SOLITONS; BACKLUND TRANSFORMATION; CONCATENATION MODEL; LUMP SOLUTIONS; EVOLUTION; FORM; LAW;

D O I：

10.1007/s10773-024-05565-3

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

Kadomtsev-Petviashvili (KP)-typed models are used to elucidate certain shallow water waves that arise in plasma physics, marine engineering, ocean physics, fluid dynamics, etc. In this paper, we investigate a (3+1)-dimensional KP equation for the shallow water waves: (1) Via some exchange formulae, a bilinear Backlund transformation and the corresponding soliton-like solutions are constructed. (2) Via symbolic computation, fission/fusion solutions are derived with some parameter conditions in the N-soliton solutions, which are different from those in the existing literature, where N is a positive integer. We graphically display the spatial structures of the fission/fusion waves to supplement the existing literature. (3) Periodic-wave solutions are worked out via the Hirota-Riemann method. Via the asymptotic properties, relation between the periodic-wave and one-soliton solutions is discussed.

引用

页数：15

共 77 条

[1] Stationary optical solitons with nonlinear chromatic dispersion for Lakshmanan-Porsezian-Daniel model having Kerr law of nonlinear refractive index [J].