Vectorial approach to coupled nonlinear Schrödinger systems under nonlocal Cauchy conditions

Abstract

The paper presents a vectorial approach for coupled general nonlinear Schrödinger systems with nonlocal Cauchy conditions. Based on fixed-point principles, the use of matrices with spectral radius less than one, and on basic properties of the Schrödinger solution operator, several existence results are obtained. The essential role of the support of the nonlocal Cauchy condition is emphasized and fully exploited.

Keywords:

• nonlinear Schrödinger equation
• nonlocal condition
• coupled system
• global existence
• nonlinear operator
• fixed point

AMS Subject Classifications:

• 35Q55
• 47J35
• 35B45

Dislosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Both authors acknowledge the support from the French grant ANR-12-MONU-0007-02 BECASIM. The second author was also partially supported by a grant of the Romanian National Authority for Scientific Research, CNCS – UEFISCDI, project number PN-II-ID-PCE-2011-3-0094.