Positons for the Toda lattice and related spectral problems
Positons for the Toda lattice and related spectral problems
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DOI：
10.1088/0305-4470/28/7/017
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发表时间：
1995-04
期刊：
影响因子：
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通讯作者：
A. Stahlhofen;V. Matveev
中科院分区：
文献类型：
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作者：
A. Stahlhofen;V. Matveev
对于Toda晶格方程，引入了正电子的概念。结果表明，当这些多参数振荡和慢衰减解作为势函数插入到相应Lax对的有限差分薛定谔方程中时，得到一个平凡的S矩阵。所得到的特征值被嵌入到这个无限雅可比矩阵的连续谱中。讨论了与单正解有关的奇点，并与连续可积模型的正解的奇点进行了比较。分析了孤子-正子相互作用的特点。
The concept of positons is introduced for the Toda lattice equation. It is shown that these multiparametric oscillating and slowly decaying solutions, when inserted as potentials in the finite-difference Schrodinger equation of the corresponding Lax pair, lead to a trivial S-matrix. The resulting eigenvalues are embedded in the continuous spectrum of this infinite Jacobi matrix. The singularities connected with the one-positon solution are discussed and compared with those of the positons of continuous integrable models. The special features of the soliton-positon interaction are analysed.