An extended representation of three spin component Bose Einstein Condensate solitons

TL;DR

This paper introduces a new symmetric representation for three-component Bose-Einstein condensate solitons, enabling analysis beyond integrable cases and revealing a new class of solutions.

Contribution

It provides a simple symmetric representation for N=1 solitons in three-component BECs, extending analysis to nonintegrable coupling constants.

Findings

Exact N soliton solutions for special coupling ratios

A new symmetric representation for solitons

Discovery of a new class of solutions in nonintegrable cases

Abstract

We consider a three spin component Bose Einstein Condensate as described by as many coupled nonlinear Schroedinger equations. For a very special ratio of the coupling constants, exact N soliton solutions to this set of equations are known. Here we find a simple representation including the N = 1 solution based on the symmetry of the equations. This symmetry is described by a linear operator, the nonlinearity of NLS notwithstanding. Our useful representation opens the door to the nonintegrable case of general coupling constants. A new class of solutions is found.