Construction Of New Exact Solutions For Five Nonlinear Partial Differential Equations

Construction of exact solutions of nonlinear partial diierentialequations is a significant problem of diierential equations and computeralgebra.In this paper, we will use the (GG )-expansion method, modified (GG )-expansion method, the new expansion method with using generalized Riccatiequation and improved generalized auxiliary diierential equation method toestablish the new exact solutions for five nonlinear partial diierential equations.These five equations include: (1)the dispersive water wave equation, (2)gener-alized variable coeicient Gardner equation, (3)Sharma-Tasso-Olver equation,(4)a class of nonlinear partial diierential equations which can evolve intoφ4equation, Klein-Gordon equation, Duing equation, Landan-Ginburg-Higgsequation and Sine-Gordon equation, (5)generalized Zakharov-Kuznetsov (Z-K)equation. A series of new exact solutions which include rational functionsolutions, trigonometric function solutions, soliton solutions and hyperbolicfunction solutions are obtained.