Rogue waves in nonlinear Schrödinger models with variable coefficients: Application to Bose–Einstein condensates

2013/11/30 by Jingsong He, J. S. He, E. G. Charalampidis +2
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #nlin.PS

paper · pdf · doi:10.1016/j.physleta.2013.12.002

published as Phys. Lett. A 378 (2014) · 15 pages, 30 figures

openalex publication_date 2013/12/06 · arxiv created 2014/10/22 · arxiv updated 2014/10/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We explore the form of rogue wave solutions in a select set of case examples of nonlinear Schrödinger equations with variable coefficients. We focus on systems with constant dispersion, and present three different models that describe atomic Bose-Einstein condensates in different experimentally relevant settings. For these models, we identify exact rogue wave solutions. Our analytical findings are corroborated by direct numerical integration of the original equations, performed by two different schemes. Very good agreement between numerical results and analytical predictions for the emergence of the rogue waves is identified. Additionally, the nontrivial fate of small numerically induced perturbations to the exact rogue wave solutions is also discussed.

Citations

• Matter rogue wave in Bose-Einstein condensates with attractive atomic interaction
• Tuning the Scattering Length with an Optically Induced Feshbach Resonance
• Rogue waves in the atmosphere
• Nonlinearity Management in Optics: Experiment, Theory, and Simulation
• The Perturbed Plane‐Wave Solutions of the Cubic Schrödinger Equation
• Solving Ordinary Differential Equations I