Exact periodic and solitonic states in the spinor condensates

TL;DR

This paper introduces an analytical method to find exact periodic and solitonic solutions for one-dimensional spinor Bose-Einstein condensates described by coupled nonlinear Gross-Pitaevskii equations, applicable to F=1 and F=2 systems.

Contribution

The authors derive a general, approximation-free set of exact solutions for spinor condensates, expanding the understanding of their nonlinear dynamics in uniform potentials.

Findings

Derived multiple classes of exact solutions for F=1 and F=2 condensates.

Solutions include both real and complex periodic and solitonic states.

No approximations or parameter constraints are required for these solutions.

Abstract

We propose a method to analytically solve the one-dimensional coupled nonlinear Gross-Pitaevskii equations which govern the motion of the spinor Bose-Einstein condensates. In a uniform external potential, the Hamiltonian comprises the kinetic energy, the linear and the quadratic Zeeman energies. Several classes of exact periodic and solitonic solutions, either in real or in complex forms, are obtained for both the F=1 and F=2 condensates. These solutions are general that contain neither approximations nor constraints on the system parameters.