Lie symmetry reductions and dynamics of solitary wave solutions of breaking soliton equation

In this paper, some new invariant solutions of breaking soliton (BS) equation have been derived by using similarity transformations method. The system represents the interaction of Riemann waves propagating along [Formula: see text]-axis and long waves along [Formula: see text]-axis. The commutative relation and symmetry analysis of BS equation are derived using Lie group theory. Meanwhile, the method reduces the number of independent variables by one in each step. A repeated application of similarity transformations method reduces the BS equation into overdetermined equations, which provide invariant solutions. The derived results are more general than previous findings. The obtained solutions are supplemented by numerical simulation, which makes this research physically meaningful. Eventually, doubly soliton, multisoliton and asymptotic profiles of solutions are analyzed in the analysis and discussion section.