Peaked Traveling Wave Solutions To A Generalized Novikov Equation With Cubic And Quadratic Nonlinearities

The Camassa-Holm equation, Degasperis-Procesi equation and Novikov equation arethe three typical integrable evolution equations admitting peaked solitons. In this paper,a generalized Novikov equation with cubic and quadratic nonlinearities is studied, which isregarded as a generalization of these three well-known studied equations. It is shown thatthis equation admits single peaked traveling wave solutions, periodic peaked traveling wavesolutions and multi-peaked traveling wave solutions.An outline of this thesis is as follows:Chapter1is a preliminary chapter, which encompasses the background and history ofthese three related integrable system§and give some famous functions which include theirfeatures.In Chapter2, it first shows a formulation to the weak solutions of Eq., which will beused in the subsequent sections. The conservation laws of Eq. which for certain constantsa2and a3are obtained. and then§we discuss the existence of single peaked traveling wavesolutions. It is shown that when the wave speed c satisfies a23+4a1c>0, there exist singlepeaked traveling wave solutions.In Chapter3, the multi-peaked traveling wave solutions are obtained.And,the two-peaked traveling wave solutions are also obtained which for some simple combination e-quations.In Chapter4,it first shows a formulation to the weak solutions of Eq in periodic case.Then,theexistence of periodic peaked traveling wave solutions will be obtained.At last§the analysiswill be given in brief.In Chapter5,makes a summary and discusses what can be done in the future.