Analysis of non-linear Klein-Gordon equations using Lie symmetry

被引：22

作者：

Khalique, Chaudry Masood ^{[1
]}

Biswas, Anjan ^{[1
]}

机构：

[1] North West Univ, Int Inst Symmetry Anal & Math Modeling, Dept Math Sci, ZA-2735 Mmabatho, South Africa

来源：

APPLIED MATHEMATICS LETTERS | 2010年 / 23卷 / 11期

关键词：

Integrability; Lie symmetry;

D O I：

10.1016/j.aml.2010.07.006

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This work obtains the stationary solutions of the non-linear Klein-Gordon equations in 1 + 1 dimensions. The technique that is used to carry out the analysis is the Lie symmetry approach. There are five types of non-linearity that are studied in this work. In each case, the analysis yields non-trivial stationary solutions; it is the first time that this has been seen. (C) 2010 Elsevier Ltd. All rights reserved.

引用

页码：1397 / 1400

页数：4

共 50 条

[1] NON-LINEAR KLEIN-GORDON EQUATIONS AND SIMPLE LIE-ALGEBRAS
FORDY, AP
GIBBONS, J
[J]. PROCEEDINGS OF THE ROYAL IRISH ACADEMY SECTION A-MATHEMATICAL AND PHYSICAL SCIENCES, 1983, 83 (01) : 33 - 44
[2] STABLE STANDING WAVES OF NON-LINEAR KLEIN-GORDON EQUATIONS
SHATAH, J
[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1983, 91 (03) : 313 - 327
[3] CLASS OF NON-LINEAR KLEIN-GORDON EQUATIONS WITH LOCALIZED SOLUTIONS
MORRIS, TF
[J]. PHYSICS LETTERS B, 1978, 78 (01) : 87 - 89
[4] On the standing wave in coupled non-linear Klein-Gordon equations
Zhang, J
[J]. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2003, 26 (01) : 11 - 25
[5] INTEGRABLE NON-LINEAR KLEIN-GORDON EQUATIONS AND TODA-LATTICES
FORDY, AP
GIBBONS, J
[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1980, 77 (01) : 21 - 30
[6] ON THE INSTABILITY OF STATIONARY STATES IN NON-LINEAR SCHRODINGER OR KLEIN-GORDON EQUATIONS
BERESTYCKI, H
CAZENAVE, T
[J]. COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1981, 293 (09): : 489 - 492
[7] ON LP-DECAY AND SCATTERING FOR NON-LINEAR KLEIN-GORDON EQUATIONS
BRENNER, P
[J]. MATHEMATICA SCANDINAVICA, 1982, 51 (02) : 333 - 360
[8] Numerical solution of non-linear Klein-Gordon equations by variational iteration method
Abbasbandy, Saeid
[J]. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 2007, 70 (07) : 876 - 881
[9] NON-DISSIPATIVE CHARACTER OF SOLUTIONS OF A CLASS OF NON-LINEAR KLEIN-GORDON EQUATIONS
MORRIS, TF
[J]. PHYSICS LETTERS B, 1978, 76 (03) : 337 - 339
[10] SCATTERING OF SOLUTIONS OF NON-LINEAR KLEIN-GORDON EQUATIONS IN 3 SPACE DIMENSIONS
TSUTSUMI, M
[J]. JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 1983, 35 (03) : 521 - 538

← 1 2 3 4 5 →