Remarks on derivative nonlinear Schr\"odinger systems with multiple masses

TL;DR

This paper establishes global existence and asymptotic behavior of small solutions for derivative nonlinear Schrödinger systems with multiple masses under non-resonance conditions, extending previous work on the resonant case.

Contribution

It provides the first analysis of global solutions and asymptotics for non-resonant derivative Schrödinger systems with multiple masses, complementing prior resonant case studies.

Findings

Proved global existence of small solutions

Analyzed large-time asymptotics of solutions

Extended understanding from resonant to non-resonant mass cases

Abstract

We prove global existence of small solutions to the initial value problem for a class of cubic derivative nonlinear Schr\"odinger systems with the masses satisfying suitable non-resonance relations. The large-time asymptotics of the solutions are also shown. This work is intended to provide a counterpart of the previous paper (arXiv:1507.07617) in which the mass resonance case was treated.