On Lie symmetries, optimal systems and explicit solutions to the Kudryashov-Sinelshchikov equation

被引：82

作者：

Tu, Jian-Min ^{[1
,2
]}

Tian, Shou-Fu ^{[1
,2
,3
]}

Xu, Mei-Juan ^{[1
,2
]}

Zhang, Tian-Tian ^{[1
,2
,3
]}

机构：

[1] China Univ Min & Technol, Dept Math, Xuzhou 221116, Peoples R China

[2] China Univ Min & Technol, Ctr Nonlinear Equat, Xuzhou 221116, Peoples R China

[3] Univ Cambridge, Dept Appl Math & Theoret Phys, Cambridge CB3 0WA, England

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2016年 / 275卷

关键词：

Kudryashov-Sinelshchikov equation; Lie symmetry analysis; Power series method; Similarity reduction; Exact solutions; PERIODIC-SOLUTIONS; CONSERVATION-LAWS; INTEGRABILITY; EVOLUTION; SOLITONS; WAVES;

D O I：

10.1016/j.amc.2015.11.072

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Under investigation in this paper is the Kudryashov-Sinelshchikov equation, which describes influence of viscosity and heat transfer on propagation of the pressure waves. The Lie symmetry method is used to study its vector fields and optimal systems, respectively. Furthermore, the symmetry reductions and exact solutions of the equation are obtained on the basic of the optimal systems. Finally, based on the power series theory, a kind of explicit power series solutions for the equation is well constructed with a detailed derivation. (C) 2015 Elsevier Inc. All rights reserved.

引用

页码：345 / 352

页数：8

共 34 条

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