Two-Component Nonlinear Schrödinger Equations for Spin-1 BECs

Wu‐Ming Liu, Emmanuel Kengne

G R W Quispel

It is shown that the equation of motion for the classical continuous Heisenberg spin chain with uniaxial anisotropy is obtained as a reduction of the two-component derivative nonlinear Schrodinger equation.

Chris Hamner, JiaJia Chang, Peter Engels

Paulsamy Muruganandam, M. Lakshmanan

This chapter focuses on exploring localized excitations in the variable coefficient nonlinear Schrodinger (NLS) equation and its generalizations. The motivation comes from the fact that the NLS equation and its variants appear in several branches/topics of physics, including nonlinear optics and Bose-Einstein condensates (BECs). The chapter reviews critically the variety of matter wave solitons and their interactions in single- and multi-component Bose-Einstein condensates. It provides a brief overview of the mean Gross- Pitaevskii (GP) equation, derivation of the one-dimensional GP equation, and mapping of the 1D GP equation to the standard NLS equation. The chapter discusses matter wave single and multi bright and dark solitons of Bose– Einstein condensates with varying trap potentials and atomic interactions. It shows various solitons solutions of multi-component BECs described by the two coupled GP equations. In this case, the coupled GP equation has been mapped onto a two coupled NLS equation.

Nikolay A. Kostov, Vladimir Stefanov Gerdjikov, V. Z. Enolski +2 more

Coupled nonlinear Schrödinger equations (CNLS) with an external elliptic function potential model a quasi one-dimensional interacting two-component Bose-Einstein condensate trapped in a standing light wave. New stationary solutions of the CNLS with a periodic potential are derived and interpreted as exact Bloch states at the edge of the Brillouin zone. The modulationally unstable solutions lead to formation of localized ground states of the coupled BEC system.

Andrei Ludu