Three wave interaction solitons for an energy critical Schr\"odinger system

TL;DR

This paper studies a three-wave interaction Schr"odinger system modeling Raman amplification, revealing existence of stable and unstable standing waves, global solutions, and absence of small data scattering, highlighting unique features of three-wave interactions.

Contribution

It demonstrates novel phenomena in a three-wave energy critical Schr"odinger system, differing from classical models, and connects theoretical results with experimental observations.

Findings

Existence of stable and unstable standing waves

Global solutions are established

Small data scattering is absent

Abstract

We investigate standing waves for the energy critical Schr\"odinger system with three waves interaction arising as a model for the Raman amplification in a plasma. Several results are proved: simultaneous existence of stable and unstable standing waves, existence of global solutions, and absence of small data scattering. Our main results show some specific features arising from the three waves interaction differently from the classical energy critical Schr\"odinger equation, and they support some experimental observations on Raman amplification.