Scattering of Solitons and Dark Solitons by Potential Walls in the Nonlinear Schroedinger Equation

Abstract

Scattering of solitons and dark solitons by potential walls is studied in the nonlinear Schroedinger equation under various conditions. We investigate the conditions under which solitons are split into two solitons at the potential wall. We find that a soliton can be trapped in an interspace between two potential walls. A dark soliton can also be scattered at the potential wall. Similarly to a bright soliton, a dark soliton can pass through more easily the potential wall, as the width of the dark soliton is larger. A dark soliton can run away spontaneously from an interspace between the two potential walls. We also study the motion of a two-dimensional soliton in a two-dimensional quintic nonlinear Schroedinger equation. We find the coherent tunneling through a potential wall, and the refraction corresponding to Newton's refraction theory.

arXiv comment13 pages, 8 figures

References in corpus (7)

• Formation and Propagation of Matter Wave Soliton Trains
• Formation of a Matter-Wave Bright Soliton
• Dark Solitons in Bose-Einstein Condensates
• Discrete Solitons and Breathers with Dilute Bose-Einstein Condensates
• Motion of dark solitons in trapped Bose-Einstein condensates
• Regular spatial structures in arrays of Bose-Einstein condensates induced by modulational instability
• Scattering and Trapping of Nonlinear Schroedinger Solitons in External Potentials

Cited by in corpus (7)

• Soliton-based matter wave interferometer
• Two-dimensional dark soliton in the nonlinear Schroedinger equation
• Particle-wave duality in quantum tunneling of a bright soliton
• Interactions of bright and dark solitons with localized $\mathcal{P}\mathcal{T}$-symmetric potentials
• Dark solitons near potential and nonlinearity steps
• High-speed soliton ejection generated from the scattering of bright solitons by modulated reflectionless potential wells
• Power dependent switching of nonlinear trapping by local photonic potentials