On global attractors for 2D damped driven nonlinear Schrödinger equations

Abstract

The well-posedness and global attraction are proved for nonautonomous 2D nonlinear damped Schrödinger equations with almost periodic external source in a bounded region. The proofs rely on a development of the method of energy equation. The research is inspired by the problems of laser and maser coherent radiation.

Keywords:

• Nonlinear Schrödinger equation
• Galerkin approximations
• energy equation
• absorbing set
• global attractor
• almost periodic function

2020 Mathematics Subject Classifications:

• 35B41
• 35Q40
• 35Q41
• 42A75
• 37N20
• 78A60

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The research is supported by the Austrian Science Fund (FWF) [grant numbers P28152–N35 and P34177–N].