Orbital Stability Of Periodic Waves For The Klein-gordon-schrödinger System

This article deals with the existence and orbital stability of a two- parameter family of periodic traveling-wave solutions for the Klein-Gordon- Schrödinger system with Yukawa interaction. The existence of such a family of periodic waves is deduced from the Implicit Function Theorem, and the orbital stability is obtained from arguments due to Benjamin, Bona, and Weinstein.311221238Angulo Pava, J., Nonlinear stability of periodic traveling wave solutions to the Schr̈odinger and modified Korteweg-de Vries equations (2007) J. Differential Equations, 235, pp. 1-30Angulo Pava, J., Bona, J.L., Scialom, M., Stability of cnoidal waves (2006) Adv. Differential Equations, 11, pp. 1321-1374Angulo Pava, J., Matheus, C., Pilod, D., Global well-posedness and non-linear stability ofperiodic traveling waves for a Schr̈odinger-Benjamin-Ono system (2009) Commun. Pure Appl. 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