The Numerical Investigation To Some Nonlinear Evolution Equations

Recently, the nonlinear science is rapidly developing and has become the frontierof modern science and technology. In the research of the nonlinear science, it is a stilldifficult and hot topic to derive solution of the nonlinear equation. Solving solitonequation and differential-integral equation is one of the most important fields of thenonlinear science. Due to the diversity and complexity of soliton equation anddifferential-integral equation, there are few soliton equations and differential-integralequations which can obtain the exact solutions, thus looking for efficient numerical orapproximate method is one of the important research fields.In this paper, finite difference method and Runge-Kutta method are used todiscuss the numerical solutions of two Burgers kind equations and simulate thenumerical solutions. And then using the variational iterative algorithm, theapproximate solution of the FKPP equation is obtained, and influence on the accuracyof the approximate solution nonlinearity to FKPP equation is studied. The numericalsimulation and the approximate solution are very important in theory and practice.In Chapter1, the development of nonlinear science is firstly made a summary,and then summarizes the soliton, soliton theory and the development of nonlinearapproximate solution.In Chapter2, finite difference method, Runge-Kutta method, variational iterativemethod was introduced.In Chapter3, two kind of Burgers equation of numerical simulation waspresented by finite difference and diagonal implicit Runge-Kutta-Nystrom (DIRKN)method, the method is illustrated based effective, directly, etc. by simulation graphicsand error.In Chapter4, approximate solution and analysis of FKPP equations waspresented by the variational iterative method. In Chapter5, the major conclusions of this thesis are made, and the prospects ofthe numerical solution and approximate solution for nonlinear evolution equations areanalysed.