Nonlinear Stability of Periodic Traveling Wave Solutions for (n+1)-Dimensional Coupled Nonlinear Klein-Gordon Equations

被引：0

作者：

Sun, Cong ^{[1
]}

Jiang, Bo ^{[2
]}

机构：

[1] Jilin Univ, Coll Math, Changchun 130012, Peoples R China

[2] Jilin Jianzhu Univ, City Coll, Changchun 130111, Peoples R China

来源：

MATHEMATICAL PROBLEMS IN ENGINEERING | 2015年 / 2015卷

关键词：

ELLIPTIC FUNCTION EXPANSION; STANDING WAVES; SOLITARY WAVES; INSTABILITY;

D O I：

10.1155/2015/546121

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

We study the existence and orbital stability of smooth periodic traveling waves solutions of the (n + 1)-dimensional coupled nonlinear Klein-Gordon equations. Such a system occurs in quantum mechanics, fluid mechanics, and optical fiber communication. Inspired by Angulo Pava's results (2007), and by applying the stability theory established by Grillakis et al. (1987), we prove the existence of periodic traveling waves solutions and obtain the orbital stability of the solutions to this system.

引用

页数：7

共 19 条

[1] TOTAL POSITIVITY AND THE STABILITY OF INTERNAL WAVES IN STRATIFIED FLUIDS OF FINITE DEPTH [J].

ALBERT, JP ;

BONA, JL .

IMA JOURNAL OF APPLIED MATHEMATICS, 1991, 46 (1-2) :1-19

[2]

Angulo J., 2009, Math Surveys and Monographs, V156

[3]

Angulo J., 2004, MAT CONT, V27, P189

[4] STABILITY OF SOLITARY WAVES [J].

BENJAMIN, TB .

PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL AND PHYSICAL SCIENCES, 1972, 328 (1573) :153-+

[5]

Byrd P. F., 1971, Handbook of Elliptic Integrals for Engineers and Scientists

[6] Extended tanh-function method and its applications to nonlinear equations [J].

Fan, EG .

PHYSICS LETTERS A, 2000, 277 (4-5) :212-218

[7] New Jacobi elliptic function expansion and new periodic solutions of nonlinear wave equations [J].

Fu, ZT ;

Liu, SK ;

Liu, SD ;

Zhao, Q .

PHYSICS LETTERS A, 2001, 290 (1-2) :72-76

[8] GLOBAL SOLUTION OF THE SYSTEM OF WAVE AND KLEIN-GORDON EQUATIONS [J].

GEORGIEV, V .

MATHEMATISCHE ZEITSCHRIFT, 1990, 203 (04) :683-698

[9] STABILITY THEORY OF SOLITARY WAVES IN THE PRESENCE OF SYMMETRY .2. [J].

GRILLAKIS, M ;

SHATAH, J ;

STRAUSS, W .

JOURNAL OF FUNCTIONAL ANALYSIS, 1990, 94 (02) :308-348

[10] STABILITY THEORY OF SOLITARY WAVES IN THE PRESENCE OF SYMMETRY .1. [J].

GRILLAKIS, M ;

SHATAH, J ;

STRAUSS, W .

JOURNAL OF FUNCTIONAL ANALYSIS, 1987, 74 (01) :160-197

← 1 2 →