Bound states spectrum of the nonlinear Schrödinger equation with Pöschl-Teller and square potential wells

2022/01/07 by L. Al Sakkaf, Sakkaf, L. Al, U. Al Khawaja +1 · 1 citation
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #Mechanical and Optical Resonators #Nonlinear Photonic Systems #Pattern Formation and Solitons (nlin.PS)

paper · pdf · doi:10.48550/arxiv.2201.02678

openalex publication_date 2022/01/07 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28

Abstract

We obtain the spectrum of bound states for a modified P"oschl-Teller and square potential wells in the nonlinear Schr"odinger equation. For a fixed norm of bound states, the spectrum for both potentials turns out to consist of a finite number of multi-node localized states. We use modulational instability analysis to derive the relation that gives the number of possible localized states and the maximum number of nodes in terms of the width of the potential. Soliton scattering by these two potentials confirmed the existence of the localized states which form as trapped modes. Critical speed for quantum reflection was calculated using the energies of the trapped modes.

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