The Traveling Wave Solutions And Exact Solutions Of Two Classes Of Partial Differential Equations

Traveling wave solutions and exact solutions of nonlinear partial differential equations are an important area of research in nonlinear sciences.The Schr?dinger equation is widely used in quantum mechanics,atomic physics,nuclear physics,solid state physics and modern molecular biology.The Black-Scholes equation has a classic application in stocks and bonds in the option pricing model.Based on the traveling wave transformation,the first integral method and the G'/G-expansion method are used to consider the traveling wave solution equations and the exact solutions of a class of Schr?dinger type equation and a class of generalized Black-Scholes equation.Based on the traveling wave solutions equations,by using the first integral method,the traveling wave solution equations and the exact solutions of the two classes of equations are found;Using the qualitative theory of differential equations,traveling wave solutions of the class of Schr?dinger type equation are obtained;By using the G'/G-expansion method,traveling wave solutions to this generalized Black-Scholes equation are given.