Asymptotic behavior of solutions to a system of Schrodinger equations

Abstract

This article concerns the behaviour of solutions to a coupled system of Schrodinger equations that has applications in many physical problems, especially in nonlinear optics. In particular, when the solution exists globally, we obtain the growth of the solutions in the energy space. Finally, some conditions are also obtained for having blow-up in this space.

Keywords

• Coupled Schrodinger system
• energy conservation
• global solution
• growth of solutions
• blow-up
• well-posedness