Applications of the functional variable method for finding the exact solutions of nonlinear evolution equations in mathematical physics

Abstract

In this paper, the functional variable method is proposed to seek the exact solutions of some nonlinear evolution equations. The validity and advantages of the proposed method is illustrated by the applications to the Asymmetric Nizhnik-Novikov-Vesselov equation, the breaking soliton equation, the Nizhnik-Novikov-Vesselov equation and the Painlevé integrable Burgers equations, which play an important role in mathematical physics. It is shown that the proposed method provides a very effective and powerful tool for solving nonlinear evolution equations.