Title: Periodic pulses of coupled nonlinear Schrodinger equations in optics

Authors: Jaime Angulo Pava and Felipe Linares

Issue: Volume 56 (2007), Issue 2, 847-878

Abstract: A system of coupled nonlinear Schr\"odinger equations arising in nonlinear optics is considered. The existence of periodic pulses as well as the stability and instability of such solutions are studied. It is shown the existence of a smooth curve of periodic pulses that are of cnoidal type. The Grillakis, Shatah and Strauss theory is set forward to prove the stability results. Regarding instability a general criteria introduced by Grillakis and Jones is used. The well-posedness of the periodic boundary value problem is also studied. Results in the same spirit of the ones obtained for single quadratic semilinear Schr\"odinger equation by Kenig, Ponce and Vega are established.