Soliton solutions of the Hirota’s system

Abstract

It is well known that nonlinear integrable systems have attracted a lot of attention among researchers. This fascinating subject of nonlinear science has branched out in almost all areas of technology and science. In nonlinear science soliton solutions play an important role. There are many ways to obtain soliton solutions of the nonlinear evolution equations, such as the Painleve analysis, the Hirota’s bilinear method, Darboux transformation (DT) and so on. Among the various methods, the DT has been proved very successful in driving different kinds of solutions for many of the integrable equations from a trivial seed. In this work, we focus on the construction soliton solutions for the 2+1-dimensional Hirota’s system, which is modified nonlinear Schrödinger equations. One-soliton solutions are obtained by means of the one-fold Darboux transformation for the 2+1-dimensional Hirota’s system.