Darboux transforms, deep reductions and solitons
Darboux transforms, deep reductions and solitons
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DOI：
10.1088/0305-4470/26/19/029
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发表时间：
1993-10
期刊：
影响因子：
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通讯作者：
S. Leble;N. V. Ustinov
中科院分区：
文献类型：
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作者：
S. Leble;N. V. Ustinov
给出了矩阵微分方程深度约化的显式形式和达布协方差性质。考虑二阶矩阵2*2谱问题.这个问题与减少限制被强加在潜力是第一个方程的Lax表示的Hirota-Satsuma系统（1981）。这两种约化情形是借助于双线性δ-形式来处理的.这些形式在限制条件下相对于达布变换的协方差给出了N-孤立子解的显式公式。特别地，得到了Hirota-Satsuma系统的双参数孤子解。这种解演化的特点是在某些参数区域出现奇异性。Yajima-Oikawa系统（1976）被给出作为该技术应用于3*3谱问题的一个例子。
Explicit formalisms for deep reductions of matrix differential equations and Darboux covariance properties are presented. The matrix 2*2 spectral problem of the second order is considered. This problem with the reduction constraints being imposed on the potentials is the first equation of the Lax representation of the Hirota-Satsuma system (1981). The two reduction cases are treated with the help of the bilinear delta -forms. The covariance of these forms with respect to the Darboux transforms under restrictions gives rise to explicit formulas of N-soliton solutions. In particular the two-parameter soliton solutions of the Hirota-Satsuma system are obtained. The specific feature of such solutions evolution is that the singularity appears in some parameter region. The Yajima-Oikawa system (1976) is given as an example of the technique application to a 3*3 spectral problem.