Lie point symmetry, conservation laws and exact power series solutions to the Fujimoto-Watanabe equation

Abstract

In this paper, the Fujimoto-Watanabe equation is studied with the help of the classical Lie point symmetry analysis method. Infinitesimal generators, the en­tire geometric vector fields and symmetry groups of the Fujimoto-Watanabe equation are given. By using symmetry reduction method, Fujimoto-Watanabe equation is reduced to nonlinear ordinary differential equations (NODEs), which has advantage to provide analytical solutions, and the exact analytical solutions are considered by virtue of the power series method. Finally, the symmetry of the Fujimoto-Watanabe equation with method of undetermined coefficients is obtained. As application, the conservation laws are constructed. It shows the integrability and the existence of soliton solutions of the Fujimoto-Watanabe equation.