李向正, 张金良, 王明亮. 用F展开法解变系数KdV方程[J]. 云南大学学报(自然科学版), 2006, 28(3): 222-226.
引用本文: 李向正, 张金良, 王明亮. 用F展开法解变系数KdV方程[J]. 云南大学学报(自然科学版), 2006, 28(3): 222-226.
LI Xiang-zheng, ZHANG Jin-liang, WANG Ming-liang. Solving KdV equation with variable coefficients by using F-expansion method[J]. Journal of Yunnan University: Natural Sciences Edition, 2006, 28(3): 222-226.
Citation: LI Xiang-zheng, ZHANG Jin-liang, WANG Ming-liang. Solving KdV equation with variable coefficients by using F-expansion method[J]. Journal of Yunnan University: Natural Sciences Edition, 2006, 28(3): 222-226.

用F展开法解变系数KdV方程

Solving KdV equation with variable coefficients by using F-expansion method

  • 摘要: 扩展了最近提出的F展开方法以构造变系数非线性演化方程更多的精确解,即将F展式中的常系数代之以变系数.作为例子,用扩展的F展开法解变系数KdV方程,得到了很丰富的精确解,特别是以2个不同的Jacobi椭圆函数表示的解.显然扩展的F展开方法也可以解其他类型的变系数非线性演化方程.

     

    Abstract: F-expansion method proposed recently is extended to construct more exact solutions of nonlinear evolution equations with variable coefficients.To be more precise,variable coefficients is used instead of constant coefficients in F-expansion.As an illustrative example,by using the extended F-expansion method KdV equation with variable coefficients is solved,an abundance of exact solutions,especially the solutions expressed by two different Jacobi elliptic functions,have been obtained.Obviously,the extended F-expansion method can be applied to solve other type of nonlinear evolution equations with variable coefficients as well.

     

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