Stability Properties of Periodic Standing Waves for the Klein-Gordon-Schrodinger System

Details Stability Properties of Periodic Standing Waves for the Klein-Gordon-Schrodinger System Stability Properties of Periodic Standing Waves for the Klein-Gordon-Schrodinger System

2009-07-13

arxiv.org/abs/0907.2142v2

Mathematics

Analysis of PDEs

To appear in CPAA

Scientific paper

We study the existence and orbital stability/instability of periodic standing wave solutions for the Klein-Gordon-Schr\"odinger system with Yukawa and cubic interactions. We prove the existence of periodic waves depending on the Jacobian elliptic functions. For one hand, the approach used to obtain the stability results is the classical Grillakis, Shatah and Strauss theory in the periodic context. On the other hand, to show the instability results we employ a general criterium introduced by Grillakis, which get orbital instability from linear instability.

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