Analytical study on a two-dimensional Korteweg–de Vries model with bilinear representation, Bäcklund transformation and soliton solutions
Analytical study on a two-dimensional Korteweg–de Vries model with bilinear representation, Bäcklund transformation and soliton solutions
复制标题
DOI：
10.1016/j.apm.2014.10.046
复制
发表时间：
2015-06
影响因子：
5
通讯作者：
Xing Lü;Fuhong Lin;Feng-Hua Qi
中科院分区：
文献类型：
--
作者：
Xing Lü;Fuhong Lin;Feng-Hua Qi
利用符号计算方法，将Bell多项式格式和双线性方法应用于二维Korteweg-de弗里斯（KdV）模型.导出了带一个辅助自变量的贝尔多项式表达式，并将其转化为双线性形式。根据主场和副场之间的耦合双场条件，构造了Bell多项式型Bäcklund变换，并将其转化为双线性变换.最后，通过求解双线性表示和BT，得到了二维KdV模型的孤子解，并进行了比较。与之相关的可积性质，如双线性表示、BT（特别是本文构造的包含自变量的Bell多项式型）和孤子解（特别是多孤子解）等，对进一步研究其他二维KdV和KdV型模型具有一定的参考价值。
With symbolic computation, Bell-polynomial scheme and bilinear method are applied to a two-dimensional Korteweg–de Vries (KdV) model, which is firstly proposed with Lax pair generating technique. Bell-polynomial expression with one auxiliary independent variable is derived and transformed into bilinear form. According to the coupled two-field conditions between the primary and replica fields, Bell-polynomial-typed Bäcklund transformations (BTs) are constructed and converted into the bilinear ones. Finally, soliton solutions of the two-dimensional KdV model are obtained (via solving the bilinear representation and BT, respectively) and compared. Such associated integrable properties as bilinear representation, BT (especially auxiliary-independent-variable-involved Bell-polynomial-typed ones constructed in this paper) and soliton solutions (especially the multi-soliton ones) may be useful for further study on other two-dimensional KdV and KdV-typed models.