The Hirota's direct method and multi-soliton solutions

Abstract

The study of soliton theory is always a major source of mathematical and physical inspiration. For the past few decades, soliton theory has attracted considerable attention in diverse physical applications and the various mathematical methods of solution. This project discusses on the direct method of Hirota to obtain the multi-soliton solutions of physically significant nonlinear waves equations. This includes equations with single bilinear form and coupled system of bilinear form, together with the use of Hirota D-operator and various types of transformation. Singularity analysis is used to formulate the suitable transformation.