On the complete group classification of the one-dimensional nonlinear Klein-Gordon equation with a delay

被引:25
作者
Long, Feng-Shan [1 ,2 ]
Meleshko, S. V. [1 ]
机构
[1] Suranaree Univ Technol, Inst Sci, Sch Math, Nakhon Ratchasima 30000, Thailand
[2] Guizhou Univ Finance & Econ, Sch Math & Stat, Guiyang 550025, Guizhou, Peoples R China
关键词
Klein-Gordon equation; delay partial differential equation; Lie group; invariant solution; REACTION-DIFFUSION EQUATIONS; FUNCTIONAL SEPARABLE SOLUTIONS; CONSTRAINTS METHOD;
D O I
10.1002/mma.3769
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
This research gives a complete Lie group classification of the one-dimensional nonlinear delay Klein-Gordon equation. First, the determining equations are derived and their complete solutions are found. Then the complete group classification and representations of all invariant solutions are obtained. Copyright (c) 2015 John Wiley & Sons, Ltd.
引用
收藏
页码:3255 / 3270
页数:16
相关论文
共 50 条
[41]   A Symmetrical Interpretation of the Klein-Gordon Equation [J].
Heaney, Michael B. .
FOUNDATIONS OF PHYSICS, 2013, 43 (06) :733-746
[42]   Boundary energy control of a system governed by the nonlinear Klein-Gordon equation [J].
Dolgopolik, Maksim ;
Fradkov, Alexander L. ;
Andrievsky, Boris .
MATHEMATICS OF CONTROL SIGNALS AND SYSTEMS, 2018, 30 (01)
[43]   Asymptotics of solutions with a compactness property for the nonlinear damped Klein-Gordon equation [J].
Cote, Raphael ;
Yuan, Xu .
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2022, 218
[44]   Differential transform method for solving the linear and nonlinear Klein-Gordon equation [J].
Kanth, A. S. V. Ravi ;
Aruna, K. .
COMPUTER PHYSICS COMMUNICATIONS, 2009, 180 (05) :708-711
[45]   Approximate Solutions to the Nonlinear Klein-Gordon Equation in de Sitter Spacetime [J].
Yazici, Muhammet ;
Sengul, Suleyman .
OPEN PHYSICS, 2016, 14 (01) :314-320
[46]   Tension spline approach for the numerical solution of nonlinear Klein-Gordon equation [J].
Rashidinia, J. ;
Mohammadi, R. .
COMPUTER PHYSICS COMMUNICATIONS, 2010, 181 (01) :78-91
[47]   Global behavior of the solutions to nonlinear Klein-Gordon equation with supercritical energy [J].
Dimova, M. ;
Kolkovska, N. ;
Kutev, N. .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2020, 487 (02)
[48]   Cornell and Coulomb interactions for the D-dimensional Klein-Gordon equation [J].
Hassanabadi, H. ;
Rahimov, H. ;
Zarrinkamar, S. .
ANNALEN DER PHYSIK, 2011, 523 (07) :566-575
[49]   Dynamical Behavior of Singular Traveling Waves of (n+1)-Dimensional Nonlinear Klein-Gordon Equation [J].
Feng, Dahe ;
Li, Jibin ;
Jiao, Jianjun .
QUALITATIVE THEORY OF DYNAMICAL SYSTEMS, 2019, 18 (01) :265-287
[50]   Auto-Backlund Transformations for a group of nonlinear Klein-Gordon equations [J].
Wang, Xiaoli .
2013 25TH CHINESE CONTROL AND DECISION CONFERENCE (CCDC), 2013, :3859-3861