Explicit solutions with non-trivial phase of the inhomogeneous coupled two-component NLS system

Abstract

In this article, we construct novel explicit solutions for nonlinear Schrödinger systems with spatially inhomogeneous nonlinearity by means of the Lie symmetry method. We focus the attention to solutions with non-trivial phase, which have been scarcely considered in the related literature. To get started, the theoretical method based on Lie symmetries is exposed, thus reducing the problem to the integrability of an ODE. The non-trivial phase introduces a singular term into the ODE. Then, the method is used to construct new families of analytical solutions. Some illustrative examples are provided.

arXiv comment21 pages, 11 figures, some corrections made and 5 new figures added

References in corpus (11)

• Theory of Bose-Einstein condensation in trapped gases
• Dynamically Stabilized Bright Solitons in a Two-Dimensional Bose-Einstein Condensate
• Lie symmetries and solitons in nonlinear systems with spatially inhomogeneous nonlinearities
• Symbiotic Solitons in Heteronuclear Multicomponent Bose-Einstein condensates
• Quasi-Periodic and Periodic Solutions for Systems of Coupled Nonlinear SCHRÖdinger Equations
• Analysis of an atom laser based on the spatial control of the scattering length
• On collapse in the nonlinear Schrodinger equation with time dependent nonlinearity. Application to Bose-Einstein condensates
• Vector solitons in nonlinear lattices
• Solitary waves in coupled nonlinear Schrodinger equations with spatially inhomogeneous nonlinearities
• Nonlinearity Management in Higher Dimensions
• Effected of Feshbach resonance on dynamics of matter waves in optical lattices