Localized structures in a saturable discrete NLS equation with next-nearest-neighbor interactions

V. M. Rothos

School of Mechanical Engineering and Laboratory of Nonlinear Mathematics, Aristotle University of Thessaloniki, Thessaloniki, Greece

Abstract: We address the existence of solitons and periodic traveling-wave solutions in a saturable discrete NLS {(}dNLS{\rm)} equation with next-nearest-neighbor interactions. Calculus of variations and Nehari manifolds are employed to establish the existence of discrete solitons. We prove the existence of periodic traveling waves studying the mixed-type functional differential equations using Palais–Smale conditions and variational methods.

Keywords: discrete nonlinear Schrödinger, solitons, traveling waves, calculus of variations.

MSC: 37K40, 35Q55, 46N20, 34K

Received: 30.12.2024
Revised: 14.02.2025

DOI: 10.4213/tmf10878

 English version: Theoretical and Mathematical Physics, 2025, 224:1, 1280–1294

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