| 广义Riccati方程有理展开法在非线性差分-微分方程中的应用 |
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| 引用本文： | 陈向华,李姝敏.广义Riccati方程有理展开法在非线性差分-微分方程中的应用[J].内蒙古大学学报(自然科学版),2009,40(2). |
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| 作者姓名： | 陈向华 李姝敏 |
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| 作者单位： | 包头师范学院数学科学学院,内蒙古,包头,014030 |
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| 基金项目： | 内蒙古高等学校科学研究项目 |
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| 摘 要： | 将广义Riccati方程有理展开法应用于求解非线性差分-微分方程.并在符号计算机系统Maple的帮助下,以离散的非线性mKdV lattice方程和离散的非线性(2+1)维Toda lattice方程为例,得到了一些新的精确解,其中包括双曲函数解和三角函数解.
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| 关 键 词： | 非线性差分-微分方程 Riccati方程 离散的非线性mKdVlattice方程 离散的非线性(2 1)维Todalattice方程 精确解 |
An Application of the Ritional Expansion Method for the Generalized Riccati Equation to the Nonlinear Difference-differential Equations |
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| CHEN Xiang-hua,LI Shu-min.An Application of the Ritional Expansion Method for the Generalized Riccati Equation to the Nonlinear Difference-differential Equations[J].Acta Scientiarum Naturalium Universitatis Neimongol,2009,40(2). |
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| Authors: | CHEN Xiang-hua LI Shu-min |
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| Abstract: | A rational expansion method for the generalized Riccati equation is presented to solve nonlinear difference-differential equation(s).The discrete nonlinear mKdV equation and the discrete nonlinear(2+1) dimensional Toda lattice equation are chosen as examples and a number of exact solutions of these equations are obtained including hyperbolic function solutions and trigonometric function solutions with the help of symbolic computation system Maple. |
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