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 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.