On conservation laws by Lie symmetry analysis for (2+1)-dimensional Bogoyavlensky–Konopelchenko equation in wave propagation

In this paper, using the Lie group analysis method, the infinitesimal generators for (2+1)-dimensional Bogoyavlensky–Konopelchenko equation are obtained. The new concept of nonlinear self-adjointness of differential equations is used for construction of nonlocal conservation laws. The conservation l...

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Bibliographic Details
Published in:Computers & mathematics with applications (1987) 2017-09, Vol.74 (6), p.1158-1165
Main Author: Ray, S. Saha
Format: Article
Language:English
Subjects:
(2+1)-dimensional Bogoyavlensky–Konopelchenko equation
Analysis
Conservation law
Conservation laws
Dependent variables
Differential equations
Infinitesimal generator
Lie groups
Lie symmetries analysis method
Mathematical analysis
Nonlinear equations
Nonlinear self-adjointness
Propagation
Symmetry
Wave propagation
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Summary:In this paper, using the Lie group analysis method, the infinitesimal generators for (2+1)-dimensional Bogoyavlensky–Konopelchenko equation are obtained. The new concept of nonlinear self-adjointness of differential equations is used for construction of nonlocal conservation laws. The conservation laws for the (2+1)-dimensional Bogoyavlensky–Konopelchenko equation are obtained by using the new conservation theorem method and the formal Lagrangian approach. Transforming this equation into a system of equations involving with two dependent variables, it has been shown that the resultant system of equations is quasi self-adjoint and finally the new nonlocal conservation laws are constructed by using the Lie symmetry operators.
ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2017.06.007