基于广义辅助方程解非线性动力系统论文.doc

天津职业技术师范大学 Tianjin University of Technology and Education 毕 业 论 文 专 业： 数学与应用数学 班级学号： 0702 – 19 学生姓名： 全文丽 指导教师： 赵小山 副教授 二〇一一年六月 天津职业技术师范大学本科生毕业论文 基于广义辅助方程解非线性动力系统 A generalized subsidiary equation method for nonlinear equations 专业班级：数学0702班 学生姓名：全文丽 指导教师：赵小山 副教授 学 院：理学院 2011年 6月 摘 要 基于辅助方程法的思想，引进新的拟设法，使之满足大部分的辅助方程，根据拟设得到一系列解的形式。然后，根据具体的方程，首先根据方程最高阶偏导数项和最高阶非线性项算出平衡参数，然后根据方程的维数确定解的形式带入辅助方程与原方程，将得到的超定方程组系数化零，整理简化，最后得到最终的解。（1+1）维KDV波速方程与（2+1）维摄动KDV方程是文中为了说明方法的有效性而举出的例子，KDV方程在实际中的应用也十分广泛，所以我们的方法能够帮助更好的解决实际问题。利用Maple及软件包，将（1+1）维KDV波速方程与（2+1）维摄动KDV方程分别求解出来，得到了许多更加精确的解，有独特解，尖端解，及周期解等多种形式。辅助方程法是一种相当完善的，很精确的解非线性偏微分方程的算法。 关键词：非线性超定方程；广义辅助方程；平衡参数；拟设法 ABSTRACT Auxiliary equation method based on the idea, the introduction of the new proposed law, so as to meet most of the auxiliary equation, according to the form proposed by a range of solutions, and then, depending on the equation, the first based on the highest order partial derivative equation and the most high-end items calculated parameters of the nonlinear term equilibrium, then the dimension of equations to determine the form of solution, into the auxiliary equation with the original equation, the resulting overdetermined set of coefficients of zero order simplification, and finally get the final solution. (1 +1)-dimensional KDV velocity equations and (2 +1)-dimensional perturbed KDV equation is the text to illustrate the effectiveness of the method and give examples, KDV equation in the practical application is very broad, so our method can help to better solve practical problems. Using Maple and the package will be (1 +1)-dimensional KDV velocity equations and (2 +1)-dimensional perturbed KDV equations were solved out, get a lot more accurate solution, a unique solution, cutting-edge solutions and periodic solutions, etc. forms. Auxiliary equation method is a very complete, more accurate algorithms for solving nonlinear partial differential equations. 朗读 显示对应的拉丁字符的拼音 字典 Key Word