Painlevé Analysis, Bäcklund Transformation, Lax Pair, Periodic- and Travelling-Wave Solutions for a Generalized (2+1)-Dimensional Hirota-Satsuma-Ito Equation in Fluid Mechanics

被引：5

作者：

Wang, Dong ^{[1
,2
]}

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

Yu, Xin ^{[1
,2
]}

Deng, Gao-Fu ^{[1
,2
]}

Liu, Fei-Yan ^{[1
,2
]}

机构：

[1] Beijing Univ Aeronaut & Astronaut, Key Lab Fluid Mech, Minist Educ, Beijing 100191, Peoples R China

[2] Beijing Univ Aeronaut & Astronaut, Natl Lab Computat Fluid Dynam, Beijing 100191, Peoples R China

来源：

QUALITATIVE THEORY OF DYNAMICAL SYSTEMS | 2024年 / 23卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Fluid mechanics; (2+1)-dimensional Hirota-Satsuma-Ito equation; Painleve analysis; Bell polynomials; Backlund transformation; Lax pair; Periodic wave solutions;

D O I：

10.1007/s12346-023-00850-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, under investigation is a generalized (2+1)-dimensional Hirota-Satsuma-Ito (HSI) equation in fluid mechanics. Motivated by its application in simulating the propagation of small-amplitude surface waves and shallow water waves, we focus on the Painleve integrability, commonly used transformation forms and analytical solutions of the HSI equation. Via the Painleve analysis, it is found that the HSI equation is Painleve integrable under certain condition. Bilinear form, Bell-polynomial-type Backlund transformation and Lax pair are constructed with the binary Bell polynomials. One-periodic-wave solutions are derived via the Hirota-Riemann method and displayed graphically. Through the polynomial-expansion method, travelling-wave solutions are obtained.

引用

页数：16

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