Orbital stability of traveling waves for the one-dimensional Gross-Pitaevskii equation
Patrick Gerard, Zhifei Zhang
TL;DR
This paper proves the nonlinear orbital stability of traveling wave solutions in the one-dimensional Gross-Pitaevskii equation using inverse scattering techniques, advancing understanding of wave stability in quantum fluids.
Contribution
It introduces a novel application of Zakharov-Shabat's inverse scattering method to establish stability of traveling waves in this context.
Findings
Proved nonlinear orbital stability of traveling waves.
Applied inverse scattering method to a nonlinear PDE.
Enhanced theoretical understanding of wave stability in quantum models.
Abstract
In this paper, we prove the nonlinear orbital stability of the stationary traveling wave of the one-dimensional Gross-Pitaevskii equation by using Zakharov-Shabat's inverse scattering method.
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Taxonomy
TopicsAdvanced Mathematical Physics Problems · Nonlinear Waves and Solitons · Nonlinear Photonic Systems