On soliton solutions and soliton interactions of Kulish-Sklyanin and Hirota-Ohta systems

TL;DR

This paper explores soliton solutions and their interactions in the Kulish-Sklyanin and Hirota-Ohta systems, revealing their connections through Lax pairs and deriving explicit N-soliton solutions using the Zakharov-Shabat dressing method.

Contribution

It introduces a new integrable reduction of the Hirota-Ohta system, linking it to the Kulish-Sklyanin system, and explicitly constructs multi-soliton solutions with detailed interaction analysis.

Findings

Derived N-soliton solutions for the systems.

Analyzed soliton interactions and phase shifts.

Established connections between different integrable systems.

Abstract

In this paper we consider a simplest two-dimensional reduction of the remarkable three-dimensional Hirota-Ohta system. The Lax pair of the Hirota-Ohta system was extended to a Lax triad by adding extra third linear equation, whose compatibility conditions with the Lax pair of the Hirota-Ohta imply another remarkable systems: the Kulish-Sklyanin system (KSS) together with its first higher commuting flow, which we can call as vector complex MKdV. This means that any common particular solution of these both two-dimensional integrable systems yields a corresponding particular solution of the three-dimensional Hirota-Ohta system. Using the dressing Zakharov-Shabat method we derive the $N$-soliton solutions of these systems and analyze their interactions, i.e. derive explicitly the shifts of the relative center-of-mass coordinates and the phases as functions of the discrete eigenvalues of the Lax operator. Next we relate to these NLEE system of Hirota--Ohta type and obtain its $N$-soliton solutions