A systematic method to construct Hirota’s transformations of continuous soliton equations and its applications

Hirota’s bilinear method is a powerful tool for obtaining a wide class of exact solutions of soliton equations. The crucial step of this method is to find a suitable dependent variable transformation, i.e. Hirota’s transformation, which transforms a soliton equation into a Hirota bilinear equation. In this paper, a systematic method to construct Hirota’s transformations of continuous soliton equations is proposed. And some examples are given to illuminate the availability of this method. In addition, a new two-soliton solution of a coupled nonlinear Schrödinger equation is obtained.