Internal dynamics and fission of pure-quartic soliton molecules

TL;DR

This paper investigates the weak interaction and stability of pure-quartic soliton molecules in a generalized nonlinear Schrödinger equation, revealing a fractal structure in their parameter space and predicting various bound states.

Contribution

It introduces an asymptotic analytical approach to describe pure-quartic soliton interactions and maps their complex bound state structures, including stability analysis and fractal organization.

Findings

Bound states of pure-quartic solitons are predicted with distinct phase differences.

Numerical analysis shows these bound states form a self-similar fractal structure.

Most bound states are unstable under small perturbations.

Abstract

We address the weak interaction of a pair of well-separated pure-quartic solitons (PQSs), which are solutions to a generalized nonlinear Schrodinger equation (NLSE) with the quartic-only dispersion. An asymptotic technique is applied to derive equations for the slow evolution of the temporal separation and phase difference of the PQSs interacting through the overlapping of their exponentially decaying oscillating tails. Based on this approach, various stationary states of bound PQS (soliton molecules) with distinct phase differences are predicted. Their stability is addressed via the numerical calculation of the eigenvalue spectrum of small perturbations, showing instability of the bound states. A systematic numerical analysis demonstrates that the parameter space of the PQS bound states is organized as a self-similar fractal structure, composed of regions populated by robustly oscillating or splitting two-soliton states. The analytical method and results reported here can be extended for bound states of two or several weakly interacting modes in other conservative and dissipative systems.