Volume 22, Issue 2, February 2015, Pages 233 - 264
Inverse Scattering Transform for the Discrete Focusing Nonlinear Schrödinger Equation with Nonvanishing Boundary Conditions
Authors
Cornelis van der Mee
Dip. Matematica e Informatica, Università di Cagliari, Viale Merello 92 09123 Cagliari, Italy.cornelis110553@gmail.com
Received 24 October 2014, Accepted 3 February 2015, Available Online 6 January 2021.
- DOI
- 10.1080/14029251.2015.1023583How to use a DOI?
- Keywords
- Inverse Scattering transform; Ablowitz-Ladik system; Discrete focusing Nonlinear Schrödinger Equation
- Abstract
In this article we develop the direct and inverse scattering theory of the Ablowitz-Ladik system with potentials having limits of equal positive modulus at infinity. In particular, we introduce fundamental eigensolutions, Jost solutions, and scattering coefficients, and study their properties.We also discuss the discrete eigenvalues and the corresponding norming constants. We then go on to derive the left Marchenko equations whose solutions solve the inverse scattering problem. We specify the time evolution of the scattering data to solve the initial-value problem of the corresponding integrable discrete nonlinear Schrödinger equation. The one-soliton solution is also discussed.
- Copyright
- © 2015 The Authors. Published by Atlantis Press and Taylor & Francis
- Open Access
- This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).
Cite this article
TY - JOUR AU - Cornelis van der Mee PY - 2021 DA - 2021/01/06 TI - Inverse Scattering Transform for the Discrete Focusing Nonlinear Schrödinger Equation with Nonvanishing Boundary Conditions JO - Journal of Nonlinear Mathematical Physics SP - 233 EP - 264 VL - 22 IS - 2 SN - 1776-0852 UR - https://doi.org/10.1080/14029251.2015.1023583 DO - 10.1080/14029251.2015.1023583 ID - vanderMee2021 ER -