Single Traveling Wave Solutions Of A Class Of Nonliner Dispersive Wave Equations

In this paper, single traveling wave solutions for a class of dispersive water wave equations are investigated. Using the factorization technique and a symmetry group of one parameter, we obtain the general solutions of these equations. Using the method of complete discrimination system for polynomial, a number of single traveling wave solutions to these nonlinear equations are obtained.In the third chapter, first, we introduce the factorization technique in some theorems. Second, under the traveling wave transformation, Fornberg-Whitham equation is reduced to an ordinary differential equation, whose general solution can be obtained using the factorization technique. Finally, we apply the change of the variable and complete discrimination system for polynomial to solve the corresponding integral and obtain the classification of all single traveling wave solutions to the Fornberg-Whitham equation.In the forth chapter, under the travelling wave transformation, general shallow wave equation is reduced to an ordinary differential equation. using a symmetry group of one parameter, this ODE is reduced to a second-order linear inho-mogeneous ODE. Furthermore, we apply the change of the varibale and complete discrimination system for polynomial to solve the corresponding integrals and obtain a number of single traveling wave solutions to general shallow wave equation.