| 一类带强色散项DGH方程的精确解 |
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| 引用本文： | 蔡国梁,王庆超,凌旭东. 一类带强色散项DGH方程的精确解[J]. 大学数学, 2008, 24(2): 121-127 |
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| 作者姓名： | 蔡国梁 王庆超 凌旭东 |
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| 作者单位： | 江苏大学,理学院,江苏,镇江,212013;江苏大学,理学院,江苏,镇江,212013;广东中南创展教育研究所,广州,510075;江苏大学,理学院,江苏,镇江,212013;中国人民解放军镇江船艇学院,数学系,镇江,212003 |
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| 基金项目： | 国家自然科学基金 , 江苏大学校科研和教改项目 |
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| 摘 要： | 利用改进的F-展开法,求出了一类带强色散项DGH方程的一系列类孤子解,三角函数周期解和有理数解,方程结合了KdV方程的线性色散项和C-H方程的非线性色散项.而且改进的F-展开法在借助于计算机符号系统Mathematica(Maple)下,操作方便,适用于大量的非线性偏微分方程(组),并有助于发现新解.
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| 关 键 词： | 改进的F-展开法 DGH方程 Riccati方程 精确解 |
| 文章编号： | 1672-1454(2008)02-0121-07 |
| 修稿时间： | 2006-04-10 |
Exact Solutions of DGH Equation with Strong Dispersive Term |
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| CAI Guo-liang,WANG Qing-chao,LING Xu-dong. Exact Solutions of DGH Equation with Strong Dispersive Term[J]. College Mathematics, 2008, 24(2): 121-127 |
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| Authors: | CAI Guo-liang WANG Qing-chao LING Xu-dong |
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| Abstract: | By using a modified F-expansion method,rich families of exact solutions of DGH equation with strong dispersive term have been obtained,including soliton-like solutions,trigonometric function solutions and rational solutions.The equation combines the linear dispersion of Korteweg-de Veris equation with the nonlinear dipersion of the Camassa-Holm equation.With the aid of computer symbolic systems(Mathematica or Maple),the method can be conveniently operated.Furthermore,the method can be applied to solve massive nonlinear PDEs(group),as well as helps us find new exact solutions. |
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| Keywords: | modified F-expansion method DGH equation Riccati equation exact solution |
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