The Exact Solution Of Several Nonlinear Differential Equations

Nonlinear problems come from the applied courses which are closely related to the practice.Dynamic mathematical models in the field of nonlinear science can be attributed to the nonlinear differential equation.The exact solutions of nonlinear differential equations can help scientists to study the wave propagations and explain natural phenomena,so finding the exact solutions of nonlinear differential equations has been one of the most important issue in the research field of differential equations.In this paper,we study the exact solutions of several nonlinear differential equations.In Chapter 1,we first introduce the solving methods of nonlinear differential equations and symmetry analysis of differential equations,and symbol calculations.In Chapter 2,we give the exact solutions and numerical examples of a(3+1)-dimensional KadomtsevPetviashvili(KP)equation based on the B?cklund transformation.In Chapter 3,we use Lou's direct method to study two(1+1)-dimensional equations with variable coefficients,namely,the(1+1)-dimensional KdV equation and the(1+1)-dimensional modified KdV equation.Moreover,we establish the relations between the solutions of differential equations with constant coefficients and the ones with variable coefficients.At last,we give the symmetry transformations and exact solutions of the two equations...