Bilinearization and new multisoliton solutions for the (4+1)-dimensional Fokas equation
Bilinearization and new multisoliton solutions for the (4+1)-dimensional Fokas equation
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DOI：
10.1007/s12043-015-1173-7
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发表时间：
2016-02
期刊：
影响因子：
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通讯作者：
Sheng Z. Zhang;Chi Tian;Wei-Yi Qian
中科院分区：
文献类型：
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作者：
Sheng Z. Zhang;Chi Tian;Wei-Yi Qian
在将可积的Kadomtsev-Petviashvili方程和Davey-Stewartson方程推广到高维非线性波动方程的过程中，得到了（4 + 1）维Fokas方程.本文正在研究该方程。Hirota的双线性方法是，第一次，用于解决这样一个高维方程。为了使Fokas方程双线性化，采用了一些适当的变换。得到了单孤子解、双孤子解和三孤子解。由此导出了一个新的n孤子解的统一公式。结果表明，在这项工作中所采用的转换起着关键的作用，在转换成广田的双线性形式的Fokas方程。
The (4 + 1)-dimensional Fokas equation is derived in the process of extending the integrable Kadomtsev–Petviashvili and Davey–Stewartson equations to higher-dimensional nonlinear wave equations. This equation is under investigation in this paper. Hirota’s bilinear method is, for the first time, used to solve such a higher-dimensional equation. In order to bilinearize the Fokas equation, some appropriate transformations are adopted. As a result, single-soliton solution, double-soliton solution and three-soliton solution are obtained. A new uniform formula ofn-soliton solution is derived from this. It is shown that the transformations adopted in this work play a key role in converting the Fokas equation into Hirota’s bilinear form.