超对称柱KdV方程的孤子的研究

发布时间：2018-04-11 11:22

  本文选题：超对称柱KdV方程 + Hirota双线性导数法　； 参考：《华东理工大学》2017年硕士论文

【摘要】：本文主要研究了超对称柱KdV方程,将非线性方程求解的三种方法,双线性导数法,双线性Backlund变换,Wronskian技巧推广到超对称柱KdV方程中。首先,我们利用直接法将柱KdV方程超对称化,得到超对称柱KdV方程。通过适当的变量变换,利用双线性导数推导出超对称柱KdV方程的双线性化,并构造出超对称柱KdV方程的单孤子解、双孤子解、三孤子解以及n孤子解的表达形式。其次,由超对称柱KdV方程的双线性形式出发,利用Wronskian行列式的性质和Laplace定理构造出具有Wronskian形式的孤子解,并验证了 Wr onskian形式的孤子解与双线性导数法求出的孤子解具有一致性。最后,以超对称柱KdV方程双线性形式为基础,利用超双线性算子的定义和相关公式,得到了超对称柱KdV方程的双线性Backlund变换,然后利用已知解构造出超对称柱KdV方程的许多解。
[Abstract]:In this paper, the KdV equation of supersymmetric cylinder is studied. The three methods of solving nonlinear equation, bilinear derivative method and bilinear Backlund transform are generalized to the KdV equation of supersymmetric cylinder.Firstly, we use the direct method to supersymmetric the column KdV equation and obtain the KdV equation of the supersymmetric column.The bilinear linearization of the supersymmetric cylindrical KdV equation is derived by proper variable transformation, and the expressions of the single soliton solution, the double soliton solution, the three-soliton solution and the n-soliton solution of the supersymmetric cylindrical KdV equation are constructed.Secondly, based on the bilinear form of supersymmetric cylindrical KdV equation, the soliton solution with Wronskian form is constructed by using the property of Wronskian determinant and Laplace theorem.It is proved that the soliton solution in Wr onskian form is consistent with the soliton solution obtained by bilinear derivative method.Finally, based on the bilinear form of the supersymmetric cylinder KdV equation, the bilinear Backlund transformation of the supersymmetric cylinder KdV equation is obtained by using the definition of the superbilinear operator and the relevant formulas. Then many solutions of the supersymmetric cylinder KdV equation are constructed by using the known solutions.
【学位授予单位】：华东理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175.29

【共引文献】

相关期刊论文 前2条

1 陈静;;隧道窑窑车热密封系统的改进[J];砖瓦;2017年02期

2 彭钒;郝玉香;;加热炉台车的密封综述[J];科技创新与应用;2015年11期

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本文编号：1735815