Ablowitz—Ladik特征值问题无反射位势的特征函数表示

EIGENFUNTION REPRESENTATION OF REFLECTLESS FOR ABLOWITZ-LADIK EIGENVALUE PROBLEM

本文研究 blowitz—Ladik 离散特征值问题.该问题首先被 Ablowitz—Ladik所研究,他们给出了该问题的反散射求解,并将其结果应用于解一类微分一差分方程。本文研究在无反射情形下位势的特征函数表示,获得了无反射情形下反散射问题的解的具体公式和位势的特征函数表示。这两个结果与连续情形及一维离散情形在某种意义下相类似。

Abiowitz-Ladik discret eiqenvalue problem is studied.This problem is first studied by Ablowitz and Ladik.Solution to inverse scattering problem is given,and the result is applied to solve some differitial-difference equations.In this paper eigenfunction representation of reflectless potential is studied.Both formulas of solution for inverse scattering problem and eigenfunction repre- sentation of Potential are found in the case of reflectless.Results are similar to the cases of continu- ous and one dimesion discret in some sense.