One-Dimensional Integrable Spinor BECs Mapped to Matrix Nonlinear Schrödinger Equation and Solution of Bogoliubov Equation in These Systems

Abstract

In this short note, we construct mappings from one-dimensional integrable spinor BECs to matrix nonlinear Schrödinger equation, and solve the Bogoliubov equation of these systems. A map of spin-$n$ BEC is constructed from the $2^n$-dimensional spinor representation of irreducible tensor operators of $so(2n+1)$. Solutions of Bogoliubov equation are obtained with the aid of the theory of squared Jost functions.

2.1 pages, JPSJ shortnote style. Published version. Note and reference added

References in corpus (2)

• Dark solitons in F=1 spinor Bose--Einstein condensate
• Inverse scattering method for square matrix nonlinear Schrödinger equation under nonvanishing boundary conditions