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用(G′/G)展开法求解非线性偏微分方程精确解
  • ISSN号：1005-3085
  • 期刊名称：工程数学学报
  • 时间：2014.6.15
  • 页码：361-370
  • 分类：O175.29[理学—数学;理学—基础数学]
  • 作者机构：[1]西北工业大学应用数学系,西安710129
  • 相关基金：国家自然科学基金（11202161;11172233;11102156）; 西北工业大学基础研究基金（GBKY1034）~~
  • 相关项目：基于符号计算的非线性孤子方程精确解及其动力学性质研究
作者： 陈妍呐|唐亚宁|徐伟|苏朋朋|
关键词： (G′, G)展开法, RICCATI方程, 非线性偏微分方程, 精确解, （G′/G）-expansion method, Riccati equation, nonlinear partial differential equations, exact solutions
中文摘要：

本文对（G′/G）展开法中的一类辅助方程—二阶线性常微分方程进行扩展求解,得到了此辅助方程更多形式的新精确解.借助Maple软件,利用此（G′/G）展开法求解了（3＋1）-维potential-YTSF方程和（2＋1）-维破裂孤子方程,得到了方程大量的新的精确解,包括含参数的双曲函数解和三角函数解.该方法直接简单并能构造出非线性偏微分方程更丰富的精确解,为求解非线性偏微分方程提供了一个更强大的方法.

英文摘要：

In this paper,an auxiliary equation for the（G′/G） expansion method,a secondorder linear ordinary differential equation is extended to solve.We get more forms of new exact solutions for the auxiliary equation.With the help of Maple,this method is applied to construct many new exact solutions of the（3 ＋ 1）-dimensional potential-YTSF equation and the（2 ＋ 1）-dimensional breaking soliton equation including the hyperbolic function solutions and the trigonometric function solutions with parameters.It provides a simple,straight-forward and more powerful way for solving nonlinear partial differential equations.

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期刊信息
  • 《工程数学学报》
  • 北大核心期刊（2011版）
  • 主管单位:教育部
  • 主办单位:西安交通大学
  • 主编：李大潜
  • 地址：西宁市咸宁西路28号西安交通大学数学与统计学院
  • 邮编：710049
  • 邮箱：jgsx@mail.xjtu.edu.cn
  • 电话：029-82667877
  • 国际标准刊号：ISSN：1005-3085
  • 国内统一刊号：ISSN：61-1269/O1
  • 邮发代号:
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  • 被引量:6741