新的双辅助微分方程展开法求色散水波方程的精确解
A New Double-Auxiliary Differential Equation Expansion Method for Exact Solutions of Dispersive Water Wave Equations
DOI: 10.12677/AAM.2020.93044, PDF,   
作者: 张 萍：成都理工大学工程技术学院，四川 乐山；孙峪怀：四川师范大学，四川 成都；罗 缝：乐山职业技术学院，四川 乐山
关键词: 双辅助方程展开法；齐次平衡法；色散水波方程；精确解；Double Auxiliary Equation Expansion Method； Homogeneous Equilibrium Method； Dispersive Water Wave Equation； Exact Solution
摘要: 本文在已有的辅助微分方程和G'/G-展开法的基础上构造新的双辅助微分方程展开法，并利用双辅助微分方程展开法求解了色散水波方程的新的精确解：双曲函数形式解、有理函数形式解、三角函数形式解、双曲函数与三角函数混合形式解、三角函数与有理函数混合形式解，该方法也可应用于求解其他非线性方程。
Abstract: Based on the existing auxiliary differential equations and G'/G-expansion method, this paper con-structs a new double auxiliary differential equation expansion method, and uses the double auxil-iary differential equation expansion method to solve new exact solutions of dispersive water wave equations: hyperbolic function formal solution, rational function formal solution, trigonometric function formal solution, hyperbolic function and trigonometric function mixed form solution, trigonometric function and rational function mixed form solution. The method can also be applied to solve other nonlinear equations.
文章引用：张萍, 孙峪怀, 罗缝. 新的双辅助微分方程展开法求色散水波方程的精确解[J]. 应用数学进展, 2020, 9(3): 366-371. https://doi.org/10.12677/AAM.2020.93044

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