Applications of Hirota Method to Nonlinear Partial Differential Equations

Abstract

Nonlinear partial differential equations (NLPDEs) are used to simulate a wide range of physical processes in the fields of physics, engineering, mechanics, biology, and chemistry and electronics science. These NLPDE-based models provide an explanation for a wide range of physical phenomena. One special kind of NLPDEs is the nonlinear Schr¨odinger equation (NLSE). A prominent description in the NLSE analysis is that soliton has been a popular subject of study for nonlinear model researchers during the last two decades. The Hirota method, a popular and reliable mathematical tool for locating soliton solutions of NLPDEs in a range of disciplines, including nonlinear dynamics, mathematical physics, and engineering sciences, requires the bilinearization of NLPDEs. In this thesis, our objective is to illustrate the Exact solutions of Chafee-Infante differential equation. We obtain lump soliton, lump soliton one kink and two kink, multiwave, periodic wave, rogue waves, periodic cross lump wave solutions, breather lump wave solutions, interaction between lump periodic kink wave. Moreover, we study on conformable fractional extended KdV model equation. We obtain some important solutions like Homoclinic breather solution, M-shaped rational solution, M-shaped rational solution one kink and two kink, multiwave, periodic cross rational solutions and periodic cross kink wave solutions.