Interaction properties of complex mKdV solitons

TL;DR

This paper investigates the interaction dynamics of complex solitons in two integrable generalizations of the mKdV equation, revealing how soliton shapes, speeds, and phase angles are affected during collisions.

Contribution

It provides a detailed analysis of two-soliton interactions in the Hirota and Sasa-Satsuma equations, highlighting differences in phase angle behavior and interaction profiles.

Findings

Soliton shapes and speeds are preserved post-collision with position shifts.

Interaction profiles depend on speed ratio and phase angle.

Phase angles remain unchanged in Hirota but shift in Sasa-Satsuma.

Abstract

Interaction properties of complex solitons are studied for the two U(1)-invariant integrable generalizations of the mKdV equation, given by the Hirota equation and the Sasa-Satsuma equation, which share the same travelling wave (single-soliton) solution having a {\em sech} profile characterized by a constant speed and a constant phase angle. For both equations, nonlinear interactions where a fast soliton collides with a slow soliton are shown to be described by 2-soliton solutions that can have three different types of interaction profiles depending on the speed ratio and the relative phase angle of the individual solitons. In all cases the shapes and speeds of the solitons are found to be preserved apart from a shift in position such that their center of momentum moves at a constant speed. Moreover, for the Hirota equation, the phase angles of the fast and slow solitons are found to remain unchanged, while for the Sasa-Satsuma equation, the phase angles are shown to undergo a shift such that the relative phase between the fast and slow solitons changes sign.