| 广义射影Riccati方程方法与(2+1)维色散长波方程新的精确行波解 |
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| 引用本文： | 智红燕,陈勇,张鸿庆.广义射影Riccati方程方法与(2+1)维色散长波方程新的精确行波解[J].数学物理学报(A辑),2005,25(7):956-964. |
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| 作者姓名： | 智红燕 陈勇 张鸿庆 |
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| 作者单位： | 大连理工大学应用数学系 大连 |116024
宁波大学数学系 宁波 |315211
中国科学院数学机械化重点实验室 北京 |100080 |
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| 基金项目： | 国家自然科学基金(10072013)和国家重点基础研究发展规划项目(G1998030600)以及中国博士后基金、浙江省自然科学基金(Y604056)资助 |
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| 摘 要： | 助于符号计算软件Maple,通过一种构造非线性偏微分方程更一般形式行波解的直接方法,即改进的广义射影Ricccati方程方法, 求解(2+1)维色散长波方程,
得到该方程的新的更一般形式的行波解, 包括扭状孤波解, 钟状解,孤子解和周期解. 并对部分新形式孤波解画图示意.
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| 关 键 词： | 广义射影Riccati方程方法 (2+1)维色散长波方程 行波解 |
Projective Riccati Equation Method and New Exact Travelling Wave Solutions for the (2+1)-dimensional Long Wave Equations |
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| ZHI Hong-Yan,CHEN Yong,ZHANG Hong-Qing.Projective Riccati Equation Method and New Exact Travelling Wave Solutions for the (2+1)-dimensional Long Wave Equations[J].Acta Mathematica Scientia,2005,25(7):956-964. |
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| Authors: | ZHI Hong-Yan CHEN Yong ZHANG Hong-Qing |
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| Abstract: | Based upon a generally projective Riccati equation method, which is a direct and unified algebraic method for constructing more general form travelling wave solutions of nonlinear partial differential equations (PDEs) and implemented in a computer algebraic system, the authors consider the (2+1)-dimensional dispersive long wave equations(DLWE). More and new general form solutions are obtained, including kink-shaped solitons,
bell-shaped solitons, singular solitons and periodic solutions.The properties of some new formal solitary wave solutions are shown by some figures. |
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| Keywords: | Projective Riccati equation methodzz (2+1)-dimensional long wave equations (DLWE)zz Exact solution zz |
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