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

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Belmonte-Beitia J., Gungor F., Torres P. J.

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, vol.53, no.1, 2020 (SCI-Expanded)

• Publication Type: Article / Article
• Volume: 53 Issue: 1
• Publication Date: 2020
• Doi Number: 10.1088/1751-8121/ab561d
• Journal Name: JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
• Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, INSPEC, zbMATH
• Istanbul Technical University Affiliated: Yes

Abstract

In this article, we construct novel explicit solutions for nonlinear Schr;dinger systems with spatially inhomogeneous nonlinearity by means of the Lie symmetry method. We focus the attention to solutions with the 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 ordinary differential equation (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.