One-Dimensional Integrable Spinor BECs Mapped to Matrix Nonlinear Schr\"odinger 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 Schr\"odinger equation, and solve the Bogoliubov equation of these systems. A map of spin-n BEC is constructed from the 2n-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.
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