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A Mel'nikov approach to soliton-like solutions of systems of discretized nonlinear Schrödinger equations

✍ Scribed by Michael Kollmann; Tassos Bountis

Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 676 KB
Volume: 113
Category: Article
ISSN: 0167-2789
DOI: 10.1016/s0167-2789(97)84201-7

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✦ Synopsis

We investigate a class of N coupled discretized nonlinear Schriidinger equations of interacting chains in ;I nonlinear lattice. which, in the limit of zero coupling. become integrable Ablowitz-Ladik differential-difference equation. We \tudl the existence of stationary localized excitations, in the form of soliton-like time-periodic states. by reducing the system to a perturbed 'N-dimensional symplectic map, whose homoclinic orbits are obtained by a recently developed Mcl'nikov analysis.

We find that, depending on the perturbation, homoclinic orbits can be accurately located from the simple /eroh oi'a Mel'niko\ vector and illustrate our results in the cases N = 2 and 3.

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