王思源, 陈浩. 求解KdV方程和mKdV方程的新方法:(g'/g^2) 展开法[J]. 华南师范大学学报(自然科学版), 2014, 46(1): 42-45.
引用本文: 王思源, 陈浩. 求解KdV方程和mKdV方程的新方法:(g'/g^2) 展开法[J]. 华南师范大学学报(自然科学版), 2014, 46(1): 42-45.
A New Method to Solve KdV and mKdV Equations by (g '/g^2) Expansion Method[J]. Journal of South China Normal University (Natural Science Edition), 2014, 46(1): 42-45.
Citation: A New Method to Solve KdV and mKdV Equations by (g '/g^2) Expansion Method[J]. Journal of South China Normal University (Natural Science Edition), 2014, 46(1): 42-45.

求解KdV方程和mKdV方程的新方法:(g'/g^2) 展开法

A New Method to Solve KdV and mKdV Equations by (g '/g^2) Expansion Method

  • 摘要: 根据(g'/g^2)展开法的相关原理和步骤,利用其求得KdV方程和mKdV方程的精确解.并在不同的情形下,得出三种通解:双曲函数通解,三角函数通解及有理函数通解.双曲函数通解中相关参数取特殊值时,得出了孤立波解.从求解KdV方程和mKdV方程的过程可以得出, 展(g'/g^2)开法与先前提出的(g'/g)展开法和其他方法具有简便,易于计算的特点,是求解非线性方程的较好选择.

     

    Abstract: Exact solutions of KdV and mKdV equations can be obtained according to (g/g2) expansion method. Three different solutions can be deduced: hyperbolic function solutions, trigonometric function solutions, and rational functional solutions. Solitary wave solutions can be calculated when special values of the hyperbolic function solutions are properly chosen. Having concluded from the solving of both equations, the (g/g2) expansion method is a well choice of solving nolinear equations which is more convenient, and easy-calculating than (g/g) expansion method and other methods mentioned before.

     

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