LIE SYMMETRY ANALYSIS TO THE WEAKLY COUPLED KAUP-KUPERSHMIDT EQUATION WITH TIME FRACTIONAL ORDER

被引：7

作者：

Wang, Zhenli ^{[1
]}

Zhang, Lihua ^{[2
]}

Li, Chuanzhong ^{[3
]}

机构：

[1] Nanjing Univ Sci & Technol, Sch Sci, Nanjing 210094, Jiangsu, Peoples R China

[2] Dezhou Univ, Sch Math Sci, Dezhou 253000, Shandong, Peoples R China

[3] Ningbo Univ, Sch Math Sci, Ningbo 315211, Zhejiang, Peoples R China

来源：

FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY | 2019年 / 27卷 / 04期

基金：

中国国家自然科学基金;

关键词：

Lie Symmetry Analysis; Time Fractional Weakly Coupled Kaup-Kupershmidt Equation; Riemann-Liouville Derivative; Erdelyi-Kober Operators; Sub-Equation Method; PARTIAL-DIFFERENTIAL-EQUATIONS; HOMOTOPY PERTURBATION METHOD; SYMBOLIC COMPUTATION; NUMERICAL-SOLUTIONS; POSITIVE SOLUTIONS; UNIQUENESS; EXISTENCE; SOLITONS; SYSTEMS;

D O I：

10.1142/S0218348X1950052X

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The aim of this paper is to apply the Lie group analysis method to the weakly coupled Kaup-Kupershmidt (KK) equation with time fractional order. We considered the symmetry analysis, explicit solutions to the weakly coupled time fractional KK (TF-KK) equation with Riemann-Liouville (RL) derivative. The weakly coupled TF-KK equation is reduced to a nonlinear ordinary differential equation (ODE) of fractional order. We solve the reduced fractional ODE using the sub-equation method.

引用

页数：10

共 44 条

[1]

Akbar A., 2018, THERM SCI, V22, P97

[2]

[Anonymous], 1994, GEN FRACTIONAL CALCU

[3] Symbolic computation of exact solutions expressible in hyperbolic and elliptic functions for nonlinear PDEs [J].

Baldwin, D ;

Göktas, Ü ;

Hereman, W ;

Hong, L ;

Martino, RS ;

Miller, JC .

JOURNAL OF SYMBOLIC COMPUTATION, 2004, 37 (06) :669-705

[4] Invariance of a partial differential equation of fractional order under the Lie group of scaling transformations [J].

Buckwar, E ;

Luchko, Y .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1998, 227 (01) :81-97

[5] Numerical solutions of coupled Burgers equations with time- and space-fractional derivatives [J].

Chen, Yong ;

An, Hong-Li .

APPLIED MATHEMATICS AND COMPUTATION, 2008, 200 (01) :87-95

[6]

Chen Y, 2008, COMMUN THEOR PHYS, V49, P839, DOI 10.1088/0253-6102/49/4/07

[7] Similarity solutions to nonlinear heat conduction and Burgers/Korteweg-deVries fractional equations [J].

Djordjevic, Vladan D. ;

Atanackovic, Teodor M. .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2008, 222 (02) :701-714

[8] The Adomian decomposition method for solving partial differential equations of fractal order in finite domains [J].

El-Sayed, A. M. A. ;

Gaber, M. .

PHYSICS LETTERS A, 2006, 359 (03) :175-182

[9] Symmetry properties of fractional diffusion equations [J].

Gazizov, R. K. ;

Kasatkin, A. A. ;

Lukashchuk, S. Yu .

PHYSICA SCRIPTA, 2009, T136

[10]

Gazizov R.K., 2007, Vestn. USATU, V9, P125, DOI DOI 10.1088/0031-8949/2009/T136/014016

← 1 2 3 4 5 →