Constructing The Exact Solitary Wave Solutions To Nonlinear Evolution Equations By Using Two Types Of Auxiliary Equations

In this paper, based on the homogeneous balance method, the tanh-function method and the auxiliary equation method, we have constructed some new exact solitary wave solutions to the nonlinear evolution equations by using two types of auxiliary equations and with the help of symbolic computation system, such as Mathematica or Maple. In chapter 1, using first type of auxiliary equation (I -1),(II -1),(III-1),(IV -1) and taking (5)-(6)as the solutions of the ordinarg differential equation, we constructed the new exact solitary wave solutions to some nonlinear evolution equations which contain odd-order, even-order or the mixed orderderivative terms. In the first section wecontrncted the new exact soliturg wave solutions of the Davey-Stewartson (DS) equations, the Kuperschmidt equation, nonlinear long wave equation, Liouville equation etc.In the second section, we constructed the new exact solitary wave solutions of some nonlinear evolution equations for example, the generalized Zakharov-Kutnetsov equation, Boussinesq equation, Modified Kadomstev-Petviashvili (mKP) equations etc. We also find some exact solitary wave solutions for sme-Gordorn type equations, nonlinear coupled Schrodinger-KdV equations that cannot be solved by using the homogeneous balance method. In the third section, the exactsolitary wave solutions of the 2+1 dimensional Benjamin-Bona-Mahoney (BBM) equation,2+l dimensional symmetric regular long wave equation and the Pochhammar-Chree equation are presented. In the fourth section ,we constructed the new types of exact solitary wave solutions of the Benjamin equation, 3+1 dimensional KP equation, generalized symmetric regularized long wave equations, Modified-Benjamin-Bona -Mahoney (mBBM) equations etc. In chapter 2, using a kind of hyperbolic-function assumption or trigonometric function assumption and the second type of auxiliary equations (V-1),(VI-1),(VI]-1),(IX-1) the new exact solitary wave solutions of the 2+1 dimensional dispersive long wave equations, 2+1 dimensional Korteweg-de Vries(KdV) equation and Benjamin-Bona-Mahoney(BBM) equation Modified-Korteweg-de Vries (mKdV) equation, Modified Kadomstev-Petviashvili(mKP) equation, nonlinear SchrOdinger equation and sine-Gordon type equation arc presented In chapter 3, the new exact solitary wave solutions of the KdV-mKdV equation, Fisher equation, nonlinear telegraphic equation, nonlinear Klein-Gordon equation are obtained by using an exponential type transformation.