Nonlocal symmetry classifications, nonlocal symmetry reductions, exact solutions and conservation laws of one-dimensional nonlinear Vakhnenko equation

Abstract

In this paper, the categorization of nonlocal symmetries of the (1+1)-dimensional nonlinear Vakhnenko equation is presented. The governing equation is turned into a set of invertibly equivalent partial differential equations (PDE) via the invertible transformation of the canonical coordinates. The nonlocal symmetries of the aforementioned PDE were derived by establishing an inverse potential system and a locally related subsystem of the system of invertibly equivalent PDEs. In addition, using similarity variables and group invariant solutions connected to nonlocal symmetry, the exact solution of the nonlinear Vakhnenkov equation is achieved. Finally, the conservation laws for the nonlinear Vakhnenko equation were developed using the multiplier method.