Phase-controlled elastic, inelastic, and coalescent collisions of two-dimensional flat-top solitons

TL;DR

This paper studies how two-dimensional flat-top solitons collide under the cubic-quintic nonlinear Schrödinger equation, revealing phase-controlled regimes from elastic to inelastic, with insights into the underlying interaction potentials and stability of merged states.

Contribution

It introduces a phase-dependent framework for understanding soliton collisions, including effective potentials and energetic analysis, advancing the control and interpretation of flat-top soliton interactions.

Findings

Collision outcomes depend on relative phase, with in-phase promoting strong interaction.

Effective phase-dependent potentials explain attraction and repulsion dynamics.

Merged states are stable due to lower energetic costs from interfacial energetics.

Abstract

We investigate elastic, inelastic, and coalescent collisions between two-dimensional flat-top solitons supported by the cubic-quintic nonlinear Schr\"odinger equation. Numerical simulations reveal distinct collision regimes ranging from nearly elastic scattering to strongly inelastic interactions leading to long-lived merged states. We demonstrate that the transition between these regimes is primarily controlled by the relative phase of the solitons at the collision point, with out-of-phase collisions suppressing overlap and in-phase collisions promoting strong interaction. Kinetic-energy diagnostics are introduced to quantitatively characterize collision outcomes and to identify phase- and separation-dependent windows of elasticity. To interpret the observed dynamics, we extract effective phase-dependent interaction potentials from collision trajectories, providing a mechanical picture of attraction and repulsion between flat-top solitons. The stability of merged states formed after strongly inelastic collisions is explained by their lower energetic cost, arising from interfacial energetics, where a balance between internal pressure and edge tension plays a central role. A variational analysis based on direct energy minimization supports this picture by revealing robust energetic minima associated with stationary two-dimensional flat-top solitons.