Some Exact Solutions Of The Kundu Equation And The Novikov Equation

Nonlinear equations are important mathematical models for describing natural phe-nomena and they are one of the forefront topics in the study of mathematical physics,especially in the study of soliton theory. We study exact solutions of two nonlinear equa-tions by using the bifurcation method of nonlinear wave, together with the software ofMathematica. The main work of this dissertation is as follows.In Chapter 2, we use the bifurcation method of nonlinear wave to study the travelingwave solutions of the Kundu equation. Via some special phase orbits, we obtain newexplicit traveling wave solutions of the Kundu equation. Our work extends some previousresults.In Chapter 3, the purpose of this paper is to extend the results on the Novikovequation with cubic nonlinearity. By applying the relationship of the solutions betweenthe Novikov equation and the nonlinear equation, and based on the bifurcation methodof nonlinear wave, we present exact traveling wave solutions of the nonlinear equation.Lastly, we construct the solutions for the Novikov equation from these traveling wavesolutions.