The Applications Of Jacobi Elliptic Function In Solving Nonlinear Evolution Equations

This thesis firstly introduced Jacobi elliptic function and its characters. Then, Jacobi elliptic function expanded methods and the situation of its evolution and extendedness currently of solving nonlinear equations were introduced. Lastly we researched the new methods of solving nonlinear evolution equations with Jacobi elliptic function. It briefly includes several following aspects:First, Jacobi elliptic function were introduced and some of its main characters were discussed simply. Thereby it was emphasized that the important of solving nonlinear evolution equations with Jacobi elliptic function.Second, Jacobi elliptic function expanded methods proposed by Liu et al and its evolution and extendedness currently including double Jacobi elliptic function expanded method and F expanded method of solving nonlinear equations were introduced.Third, the new general function transform was proposed by concluding the traveling wave solutions, some new results are obtained.Fourth, at basic of the improvement of Jacobi elliptic function expanded method, the extended Jacobi elliptic function expanded methods was proposed.Finally, a new function transform was proposed to solve nonlinear evolution equations with the help of the solutions of elliptic equation, and many new results are obtained...