Explicit solutions with non-trivial phase of the inhomogeneous coupled two-component NLS system
Mathematical Physics
2020-01-08 v2 math.MP
Exactly Solvable and Integrable Systems
Abstract
In this article, we construct novel explicit solutions for nonlinear Schr\"odinger 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.
Keywords
Cite
@article{arxiv.1909.00353,
title = {Explicit solutions with non-trivial phase of the inhomogeneous coupled two-component NLS system},
author = {J. Belmonte-Beitia and F. Güngör and P. J. Torres},
journal= {arXiv preprint arXiv:1909.00353},
year = {2020}
}
Comments
21 pages, 11 figures, some corrections made and 5 new figures added