Orbital stability and concentration of standing waves to nonlinear Schr\"odinger systems with mass critical exponent

TL;DR

This paper proves the existence and stability of standing waves in a mass critical nonlinear Schrödinger system and analyzes how these solutions concentrate as their masses approach critical values.

Contribution

It establishes the existence, orbital stability, and concentration behavior of standing waves in a mass critical nonlinear Schrödinger system, a novel analysis in this context.

Findings

Existence of standing-wave solutions as energy minimizers.

Orbital stability of these standing waves.

Concentration of minimizers near critical masses.

Abstract

For a nonlinear Schr\"odinger system with mass critical exponent, we prove the existence and orbital stability of standing-wave solutions obtained as minimizers of the underlying energy functional restricted to a double mass constraint. In addition, we discuss the concentration of a sequence of minimizers as their masses approach to certain critical masses.