Stability in the energy space for chains of solitons of the one-dimensional Gross-Pitaevskii equation

TL;DR

This paper proves the stability of multi-soliton solutions in the energy space for the one-dimensional Gross-Pitaevskii equation under conditions of distinct speeds and initial separation.

Contribution

It establishes the first rigorous stability result for sums of solitons of the 1D Gross-Pitaevskii equation with distinct speeds and initial separation.

Findings

Multi-soliton solutions are stable in the energy space.

Stability holds when solitons have distinct, non-zero speeds.

Initial spatial ordering and separation are crucial for stability.

Abstract

We establish the stability in the energy space for sums of solitons of the one-dimensional Gross-Pitaevskii equation when their speeds are mutually distinct and distinct from zero, and when the solitons are initially well-separated and spatially ordered according to their speeds.