Exact solutions and Painlevé analysis of a new (2+1)-dimensional generalized KdV equation
Exact solutions and Painlevé analysis of a new (2+1)-dimensional generalized KdV equation
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DOI：
10.1007/s11071-011-0228-7
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发表时间：
2012-06
影响因子：
5.6
通讯作者：
Yi Zhang;Yang Song;Li Cheng;Jian-Ya Ge;Wei-Wei Wei-Wei-Wei
中科院分区：
文献类型：
--
作者：
Yi Zhang;Yang Song;Li Cheng;Jian-Ya Ge;Wei-Wei Wei-Wei-Wei
主要讨论了存在双线性形式的（2+1）维广义KdV方程.我们证明了即使取任意常数ta =0，方程也不具有Painlevé性质。然而，这个结果与Radha和Lakshmanan的工作不同。此外，基于Hirota双线性方法，分别得到了周期波解的Riemann θ函数和有理解。详细分析了周期波解的渐近性质。
The new (2+1)-dimensional generalized KdV equation which exists the bilinear form is mainly discussed. We prove that the equation does not admit the Painlevé property even by taking the arbitrary constanta=0. However, this result is different from Radha and Lakshmanan’s work. In addition, based on Hirota bilinear method, periodic wave solutions in terms of Riemann theta function and rational solutions are derived, respectively. The asymptotic properties of the periodic wave solutions are analyzed in detail.