【作者】 吴国将；

【导师】 韩家骅；

【作者基本信息】 安徽大学 ， 理论物理， 2007， 硕士

【摘要】 本文首先简要介绍了Jacobi椭圆函数及其性质，然后介绍了非线性发展方程的Jacobi椭圆函数展开法和目前的一些演化和扩展情况，最后着重介绍本人对Jacobi椭圆函数在求解非线性发展方程中的应用方面所作的研究。具体概括起来包括以下几个方面：一、简要介绍Jacobi椭圆函数及其性质，从而阐述了用Jacobi椭圆函数求解非线性发展方程的优越性。二、介绍刘等人提出的Jacobi椭圆函数展开法及当前一些主要的扩展——双Jacobi椭圆函数展开法和F展开法。三、对行波变换进行归纳，提出了新的一般变换来求解非线性发展方程并得到许多新的周期波解。四、对Jacobi椭圆函数展开法进行改进和扩展，提出新的扩展的Jacobi椭圆展开法来求解非线性发展方程并得到许多新的周期波解。五、对椭圆方程进行讨论，提出新的函数变换并利用椭圆方程的解来求解非线性发展方程，从而得到大量新的周期波解。更多还原

【Abstract】 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更多还原