LIE SYMMETRY ANALYSIS, CONSERVATION LAWS AND EXACT SOLUTIONS OF FOURTH-ORDER TIME FRACTIONAL BURGERS EQUATION

被引：31

作者：

Qin, Chunyan ^{[1
,2
,3
]}

Tian, Shoufu ^{[1
,2
]}

Zou, Li ^{[4
,5
]}

Zhang, Tiantian ^{[1
,2
]}

机构：

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

[2] China Univ Min & Technol, Inst Math Phys, Xuzhou 221116, Jiangsu, Peoples R China

[3] Suzhou Univ, Sch Math & Stat, Suzhou 234000, Anhui, Peoples R China

[4] Dalian Univ Technol, Sch Naval Architecture, State Key Lab Struct Anal Ind Equipment, Dalian 116024, Peoples R China

[5] Collaborat Innovat Ctr Adv Ship & Deep Sea Explor, Shanghai 200240, Peoples R China

来源：

JOURNAL OF APPLIED ANALYSIS AND COMPUTATION | 2018年 / 8卷 / 06期

基金：

中国博士后科学基金; 中国国家自然科学基金;

关键词：

Lie group analysis method; invariance properties; sub-equation method; power series theory; conservation laws; PERIODIC-WAVE SOLUTIONS; HOMOCLINIC BREATHER WAVES; BOUNDARY VALUE-PROBLEMS; ROGUE WAVES; SOLITARY WAVES; VARIATIONAL-PROBLEMS; NOETHERS THEOREM; FORMULATION; DYNAMICS; SYSTEMS;

D O I：

10.11948/2018.1727

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, the fourth-order time fractional Burgers equation has been investigated, which can be used to describe gas dynamics and traffic flow. By employing the Lie group analysis method, the invariance properties of the equation are provided. With the aid of the sub-equation method, a new type of explicit solutions are well constructed with a detailed derivation. Furthermore, based on the power series theory, we investigate its approximate analytical solutions. Finally, its conservation laws with two kinds of independent variables are performed by making use of the nonlinear self-adjointness method.

引用

页码：1727 / 1746

页数：20

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