Soliton solutions of the (2+1)-dimensional Nizhnik-Novikov-Veselov equation via the Lie symmetry method and its stability analysis by using bifurcation theory

Abstract

Abstract The objective of the present article is to seek new explicit solutions to the (2+1)-dimensional Nizhnik-Novikov-Veselov(NNV) equation. The NNV system is highly nonlinear in nature and is a known isotropic Lax extension of the Korteweg–de Vries model. The similarity transformation method has been used to systematically reduce the NNV equation into ordinary differential equations(ODEs). The new exact solutions have been obtained by solving the obtained ODEs based on the formed relationships. The resulting soliton solutions contain some arbitrary constants and functions. The use of appropriate functions and constants highlighted that the solutions of the NNV equation might be soliton, multisoliton, parabolic, doubly soliton and trigonometric. Moreover, the stability of the corresponding dynamical system has been investigated using bifurcation theory with different parametric regions. The figures obtained during MATLAB simulation supported the dynamic features of the derived solutions. Finally, we explore incredible aspects of the exact wave solutions via phase portraits. The phase portraits validate the existence of some families of homoclinic and periodic orbits about the equilibrium points, respectively.