Quasi self-adjoint nonlinear wave equations

被引：29

作者：

Ibragimov, N. H. ^{[1
]}

Torrisi, M. ^{[2
]}

Tracina, R. ^{[2
]}

机构：

[1] Blekinge Inst Technol, Dept Math & Sci, SE-37179 Karlskrona, Sweden

[2] Univ Catania, Dipartimento Matemat & Informat, I-95124 Catania, Italy

来源：

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL | 2010年 / 43卷 / 44期

关键词：

D O I：

10.1088/1751-8113/43/44/442001

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

In this paper we generalize the classification of self-adjoint second-order linear partial differential equation to a family of nonlinear wave equations with two independent variables. We find a class of quasi self-adjoint nonlinear equations which includes the self-adjoint linear equations as a particular case. The property of a differential equation to be quasi self-adjoint is important, e. g. for constructing conservation laws associated with symmetries of the differential equation.

引用

页数：8

共 8 条

[1] A new conservation theorem [J].

Ibragimov, Nail H. .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2007, 333 (01) :311-328

[2] Integrating factors, adjoint equations and Lagrangians [J].

Ibragimov, NH .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2006, 318 (02) :742-757

[3]

Ibragimov NH, 2006, ARCH ALGA, V3, P53

[4]

Ibragimov NH., 2007, Arch. ALGA, V4, P55

[5] Differential invariants for quasi-linear and semi-linear wave-type equations [J].

Sophocleous, C. ;

Tracina, R. .

APPLIED MATHEMATICS AND COMPUTATION, 2008, 202 (01) :216-228

[6] On the linearization of semilinear wave equations [J].

Torrisi, M ;

Tracinà, R ;

Valenti, A .

NONLINEAR DYNAMICS, 2004, 36 (01) :97-106

[7]

TORRISI M, 1993, MODERN GROUP ANALYSIS: ADVANCED ANALYTICAL AND COMPUTATIONAL METHODS IN MATHEMATICAL PHYSICS, P367

[8]

Tracina R., 2004, Communications in Nonlinear Science and Numerical Simulation, V9, P127, DOI 10.1016/S1007-5704(03)00021-2

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