Mechanisms active during soliton turbulence leading to the bound state

Establish that, during evolution from multi-soliton initial states to soliton turbulence in the Schrödinger–Helmholtz equation, the resonant generation of secondary solitons, binary soliton mergers, and inter-soliton mass exchange are simultaneously active mechanisms driving the system toward the two-soliton bound state.

Background

The paper presents heuristic mechanisms inferred from targeted simulations: resonance between a primary soliton and traveling wave packets generating a secondary soliton; binary soliton mergers requiring phase synchrony; and mass transfer favoring stronger solitons during collisions. The authors conjecture that all these mechanisms operate together in turbulent multi-soliton evolutions.

A rigorous establishment of this conjunction would deepen understanding of nonintegrable soliton dynamics and explain the robust emergence of the bound state from complex initial configurations.