Results Relating to Hirota Method and Singularity Analysis on Some Nonlinear Waves Equations

Abstract

This article investigates on the connection between singularity analysis and Hirota method i.e. a direct method to obtain the multi-soliton solutions of nonlinear waves equations. This includes equations with single bilinear form and coupled system of bilinear forms, together with the use of Hirota D-operator and various types of transformation. In general, finding the proper substitution to obtain the Hirota bilinear form is not an easy task. Singularity analysis is used to formulate this suitable transformation. This analysis is applied to Korteweg-de Vries (KdV), modified KdV and nonlinear Schröedinger (NLS) equations.