Stability of multi-solitons in the cubic NLS equation

TL;DR

This paper proves the orbital stability of multi-solitons in the cubic nonlinear Schrödinger equation on the line using inverse scattering and dressing transformation methods, focusing on initial data in weighted L^2 spaces.

Contribution

It establishes the orbital stability of multi-solitons in the cubic NLS equation via inverse scattering techniques, extending stability results to weighted L^2 initial data.

Findings

Multi-solitons are orbitally stable in L^2(R) with weighted initial data.

The inverse scattering transform is effective for analyzing multi-soliton stability.

Stability results are obtained using dressing transformation methods.

Abstract

We address stability of multi-solitons in the cubic NLS (nonlinear Schr\"{o}dinger) equation on the line. By using the dressing transformation and the inverse scattering transform methods, we obtain the orbital stability of multi-solitons in the $L^2(\mathbb{R})$ space when the initial data is in a weighted $L^2(\mathbb{R})$ space.