Regular and chaotic dynamics of a matter-wave soliton near the atomic mirror

TL;DR

This paper investigates the complex dynamics of matter-wave solitons in a Bose-Einstein condensate under gravity, revealing both regular and chaotic behaviors through analytical and numerical methods.

Contribution

It introduces a combined analytical and numerical approach to analyze soliton dynamics near an atomic mirror, including chaos analysis using Poincaré maps.

Findings

Identification of nonlinear resonance in soliton amplitude-frequency characteristics

Demonstration of Hamiltonian chaos in soliton motion under gravity

Application of inverse scattering and Krylov-Bogoliubov methods to soliton dynamics

Abstract

The dynamics of the soliton in a self-attractive Bose-Einstein condensate under the gravity are investigated. First, we apply the inverse scattering method, which gives rise to equation of motion for the center-of-mass coordinate of the soliton. We analyze the amplitude-frequency characteristic for nonlinear resonance. Applying the Krylov-Bogoliubov method for the small parameters the dynamics of soliton on the phase plane are considered. Hamiltonian chaos under the action of the gravity on the Poincar\'e map are studied.