应用多项式完全判别系统方法求解时空分数阶复Ginzburg-Landau方程 |
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引用本文: | 胡艳,孙峪怀.应用多项式完全判别系统方法求解时空分数阶复Ginzburg-Landau方程[J].应用数学和力学,2021,42(8):874-880. |
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作者姓名: | 胡艳 孙峪怀 |
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作者单位: | 四川师范大学 数学科学学院, 成都 610066 |
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基金项目: | 国家自然科学基金(12071323) |
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摘 要: | 研究了时空分数阶复Ginzburg-Landau方程.首先通过分数阶复变换将时空分数阶复Ginzburg-Landau方程转化为一个常微分方程.然后将常微分方程化为初等积分形式.最后用多项式完全判别系统法求得一系列精确解,其中包含有孤立波解、有理函数解、三角函数周期解、Jacobi椭圆函数双周期解.
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关 键 词: | 时空分数阶复Ginzburg-Landau方程 多项式完全判别系统方法 精确解 |
收稿时间: | 2020-12-24 |
Solutions to Space-Time Fractional Complex Ginzburg-Landau Equations With the Complete Discrimination System for Polynomial Method |
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Institution: | School of Mathematical Sciences, Sichuan Normal University, Chengdu 610066, P.R.China |
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Abstract: | The space-time fractional complex Ginzburg-Landau equation was studied. Firstly, the space-time fractional complex Ginzburg-Landau equation was transformed into the ordinary differential equation through the fractional complex transform. Secondly, the ordinary differential equation was reduced to an elementary integral form. Finally, a series of exact solutions including solitary wave solutions, rational function type solutions, triangle function type periodic solutions, and Jacobian elliptic function doubly-periodic solutions, were constructed with the complete discrimination system for polynomial method. |
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