The Research On Solution And Appliactions Of A Kind Of Nonlinear Partial Differential Equations

Nonlinear science is fast devoloping, the research on nonlinear partial differential equations is becoming more and more. Results continuously updated. Especially now symbols calculation software development, new methods of solving is endless. Over several decades of development, many scientists in each field have done a lot of work, and found many solving method of accurate solution. But no one method is suit for all equation. Nonlinear phenomena in nature is complex and rich. For every kind equation, we are always exploring new methods to solve it constantly. So the study on each kind of equation has its significance. In this paper on the basis of the research of scholarsbefore, use the index function method, tangent function of method and another expansion method to solve nonlinear partial differential equations.And found a lot of effective methods.This paper used the computer symbol calculation software Maple, With a few nonlinear partial differential equations for research object, eapecially studied tank method and index funtion method, At last, we get rich exact solutions. Applied to kind of variable coefficient of partial differential equations. Use index function method has practical background of two classes of the classical nonlinear partial differential equations, to solve the problems for the later found a feasible method. Finally got the rich exact solution. Compares the similarities and differences among three kinds of methods, summarized situation.