Periodic pulses of coupled nonlinear Schrodinger equations in optics
Felipe Linares | Angulo, Jaime
Schrodinger equation | periodic solitary wave solutions | Stability
A system of coupled nonlinear Schrodinger equations arising in nonlinear optics is considered. The existence of periodic pulses as well as the stability and in- stability 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 prob- lem 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.