标题： 非线性薛定谔方程的精确解的对称性 显示英文标题

标题： Symmetries for exact solutions to the nonlinear Schrödinger equation

摘要： 在用三元组常数矩阵表示聚焦非线性薛定谔方程的精确解时，利用了一种特定的对称性。 因此，对于任意数量的束缚态以及任意多重性，相应的孤子解都可以用矩阵三元组以紧凑的形式明确写出。 相反地，从这样的孤子解中可以明确计算出相应的传输系数、束缚态极点、束缚态归一化常数以及相关Zakharov-Shabat系统的Jost解。 还表明这些结果适用于任何矩阵尺寸的矩阵非线性薛定谔方程。 显示英文摘要

摘要： A certain symmetry is exploited in expressing exact solutions to the focusing nonlinear Schr\"odinger equation in terms of a triplet of constant matrices. Consequently, for any number of bound states with any number of multiplicities the corresponding soliton solutions are explicitly written in a compact form in terms of a matrix triplet. Conversely, from such a soliton solution the corresponding transmission coefficients, bound-state poles, bound-state norming constants and Jost solutions for the associated Zakharov-Shabat system are evaluated explicitly. It is also shown that these results hold for the matrix nonlinear Schr\"odinger equation of any matrix size.