Integrability versus elasticity of soliton collisions

Ascertain the relationship between integrability and the elasticity of soliton collisions in nonlinear dispersive equations, determining how (and to what extent) the presence of an integrable structure governs elastic versus inelastic collision outcomes for traveling waves, including in the one-dimensional defocusing nonlinear Schrödinger equation with non-vanishing boundary conditions.

Background

In discussing multi-soliton dynamics, the paper contrasts integrable and non-integrable models. For completely integrable systems, pure multi-solitons exist and collisions are elastic, while for general (non-integrable) systems fewer results are known.

The authors highlight a broader conjectural link in the literature suggesting that integrability is tied to the nature of soliton collisions, and they note that only limited rigorous results are currently available, underscoring the open character of this question.