Dynamics of bound soliton states in regularized dispersive equations

TL;DR

This paper investigates the complex dynamics of topological solitons and their bound states in dispersive one-dimensional systems, revealing how external forces can stabilize moving soliton complexes with velocity-dependent behaviors.

Contribution

It provides analytical and numerical insights into the formation, stability, and dynamics of bound soliton states in dispersive equations, including conditions for breather excitation.

Findings

Bound soliton complexes can be stabilized by external forces.

Moving solitons emit radiation and form breathers under certain conditions.

Soliton velocities depend step-wise on external driving strength.

Abstract

The nonstationary dynamics of topological solitons (dislocations, domain walls, fluxons) and their bound states in one-dimensional systems with high dispersion are investigated. Dynamical features of a moving kink emitting radiation and breathers are studied analytically. Conditions of the breather excitation and its dynamical properties are specified. Processes of soliton complex formation are studied analytically and numerically in relation to the strength of the dispersion, soliton velocity, and distance between solitons. It is shown that moving bound soliton complexes with internal structure can be stabilized by an external force in a dissipative medium then their velocities depend in a step-like manner on a driving strength.