Shape changing and accelerating solitons in integrable variable mass sine-Gordon model

TL;DR

This paper introduces a class of integrable variable mass sine-Gordon models that feature exact soliton solutions capable of accelerating and changing shape, providing insights into inhomogeneous physical systems.

Contribution

The authors construct a new class of integrable variable mass sine-Gordon models with exact soliton solutions, enabling analysis of soliton dynamics in inhomogeneous systems.

Findings

Exact soliton solutions that accelerate and change shape

Models are integrable at classical and quantum levels

Applicable to physical systems like Josephson junctions and DNA dynamics

Abstract

Sine-Gordon model with variable mass (VMSG) appears in many physical systems, ranging from the current through nonuniform Josephson junction to DNA-promoter dynamics. Such models are usually nonintegrable with solutions found numerically or peturbatively. We construct a class of VMSG models, integrable both at classical and quantum level with exact soliton solutions, which can accelerate, change their shape, width and amplitude simulating realistic inhomogeneous systems at certain limits.