忒塔函数在求解非线性演化方程中的应用  

Application of theta functions for solving nonlinear evolution equations

作　　者：石玉仁[1] 杨红娟[1] 吕克璞[1] 段文山[1] 

机构地区：[1]西北师范大学物理与电子工程学院

出　　处：《西北师范大学学报（自然科学版）》2007年第1期29-33,86,共6页Journal of Northwest Normal University(Natural Science)

基　　金：国家自然科学基金资助项目(10247008)

摘　　要：建立了求解非线性演化方程精确解的忒塔函数展开法,并在计算机代数系统上得以实现,推导出若干非线性波方程的双周期精确解.方法的基本思路是把方程的解表示为忒塔函数构成的多项式,从而将非线性演化方程的求解问题转化为非线性代数方程组的求解问题.利用计算机代数系统可求解所得非线性代数方程组,最终得到非线性演化方程的双周期精确解.A mathematical approach called theta-funetion expansion method is presented to get the exact and doubly periodic solutions of a class of nonlinear evolution equations. This method can be performed totally on a computer algebra system such as Mathematica software. The basic thought of this method is to construct the solution of a nonlinear evolution equation by a polynomial in theta functions. Thus, one can convert the partial differential equation to a set of nonlinear algebraic equations. The exact solutions of the nonlinear evolution equation can be obtained via solving the nonlinear algebraic equations.

关 键 词：忒塔函数展开法 非线性演化方程 精确解 周期解 

分 类 号：O175.24[理学—数学]