Group Analysis and Nonlinear Self-Adjointness for a Generalized Breaking Soliton Equation

In this paper, a variable coefficient (2 + 1)-dimensional generalized breaking soliton equation is considered by means of the Lie group method. Having written an equation as a system of two dependent variables, we perform a complete group classification for the system. Consequently, for arbitrary functions, solutions of the generalized breaking soliton equation are connected with the ones of a variable coefficient Korteweg–de Vries equation by a transformation. For other cases, the reduced equations and exact solutions are constructed. Meanwhile, we prove that the system is nonlinearly self-adjoint and construct the general conservation law formulae.