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Updated: Jul 16, 2026
11:21
Cooling an Optically Trapped Ultracold Fermi Gas by Periodical Driving
Published on: March 30, 2017
Solitons in strongly driven discrete nonlinear Schrödinger-type models.
Josselin Garnier1, Fatkhulla Kh Abdullaev, Mario Salerno
1Laboratoire de Probabilités et Modèles Aléatoires and Laboratoire Jacques-Louis Lions, Université Paris VII, 2 Place Jussieu, 75251 Paris Cedex 5, France. garnier@math.jussieu.fr
Summary
This study investigates discrete solitons in damped and driven Ablowitz-Ladik and discrete nonlinear Schrödinger equations. New parametric bright solitons and cnoidal waves were discovered and their stability analyzed.
Area of Science:
- Nonlinear Physics
- Mathematical Physics
Background:
- The Ablowitz-Ladik (AL) and discrete nonlinear Schrödinger (DNLS) equations model wave propagation in discrete systems.
- Investigating these equations under damping and rapid driving reveals complex dynamics.
Purpose of the Study:
- To analyze discrete solitons in the AL and DNLS equations with damping and strong rapid drive.
- To identify new soliton types and analyze their stability properties.
Main Methods:
- Derivation of averaged parametric AL and DNLS equations.
- Application of the perturbed inverse scattering transform for analytical predictions.
- Numerical simulations of the original AL and DNLS equations.
Main Results:
- Identified an additional type of parametric bright discrete soliton.
- Characterized cnoidal waves and analyzed their stability.
- Confirmed analytical predictions through numerical simulations.
Conclusions:
- The study successfully characterized novel parametric bright discrete solitons and cnoidal waves.
- Numerical simulations validated the analytical predictions derived from the perturbed inverse scattering transform.
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