Closed form Solutions to the Integrable Discrete Nonlinear Schrödinger Equation

DOI

10.1142/S1402925112500106How to use a DOI?

Keywords

Ablowitz–Ladik model; exact solutions; Marchenko method; integrable discrete nonlinear Schrödinger equation

Abstract

In this article we derive explicit solutions of the matrix integrable discrete nonlinear Schrödinger equation by using the inverse scattering transform and the Marchenko method. The Marchenko equation is solved by separation of variables, where the Marchenko kernel is represented in separated form, using a matrix triplet (A, B, C). Here A has only eigenvalues of modulus larger than one. The class of solutions obtained contains the N-soliton and breather solutions as special cases. We also prove that these solutions reduce to known continuous matrix NLS solutions as the discretization step vanishes.

Copyright

© 2012 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/).

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TY  - JOUR
AU  - Francesco Demontis
AU  - Cornelis van der Mee
PY  - 2012
DA  - 2012/07/04
TI  - Closed form Solutions to the Integrable Discrete Nonlinear Schrödinger Equation
JO  - Journal of Nonlinear Mathematical Physics
SP  - 136
EP  - 157
VL  - 19
IS  - 2
SN  - 1776-0852
UR  - https://doi.org/10.1142/S1402925112500106
DO  - 10.1142/S1402925112500106
ID  - Demontis2012
ER  -