Stability of solitary-wave solutions of coupled NLS equations with power-type nonlinearities

TL;DR

This paper establishes the existence and stability of solitary-wave solutions in coupled nonlinear Schrödinger equations with power nonlinearities, using variational methods and concentration-compactness, extending previous results in the field.

Contribution

It provides new existence and stability results for coupled NLS equations with power nonlinearities, expanding the theoretical understanding of these solutions.

Findings

Existence of solitary waves proved via variational methods.

The set of minimizers is shown to be stable.

Extends previous results by Cipolatti, Zumpichiatti, Nguyen, Wang, and Ohta.

Abstract

This paper proves existence and stability results of solitary-wave solutions to coupled nonlinear Schr\"{o}dinger equations with power-type nonlinearities arising in several models of modern physics. The existence of solitary waves is obtained by solving a variational problem subject to two independent constraints and using the concentration-compactness method. The set of minimizers is shown to be stable and further information about the structures of this set are given. The paper extends the results previously obtained by Cipolatti and Zumpichiatti, Nguyen and Wang, and Ohta.