Nonlinear self-adjointness of the Krichever-Novikov equation

被引：10

作者：

Galiakberova, L. R. ^{[1
]}

Ibragimov, N. H. ^{[1
,2
]}

机构：

[1] Ufa State Aviat Tech Univ, Lab Grp Anal Math Models Nat & Engn Sci, Ufa, Russia

[2] Blekinge Inst Technol, Res Ctr ALGA Adv Lie Grp Anal, Dept Math & Sci, Karlskrona, Sweden

来源：

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION | 2014年 / 19卷 / 02期

关键词：

Krichever-Novikov equation; Adjoint equation; Nonlinear self-adjointness; Differential substitution;

D O I：

10.1016/j.cnsns.2013.06.011

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

It is known that the classification of third-order evolutionary equations with the constant separant possessing a nontrivial Lie-Backlund algebra (in other words, integrable equations) results in the linear equation, the KdV equation and the Krichever-Novikov equation. The first two of these equations are nonlinearly self-adjoint. This property allows to associate conservation laws of the equations in question with their symmetries. The problem on nonlinear self-adjointness of the Krichever-Novikov equation has not been solved yet. In the present paper we solve this problem and find the explicit form of the differential substitution providing the nonlinear self-adjointness. (c) 2013 Elsevier B.V. All rights reserved.

引用

页码：361 / 363

页数：3