Abstract
In the present paper, we study the orbital stability and instability of standing waves of the Klein–Gordon–Schrödinger system. Especially, we are interested in a standing wave which is expressed by the unique positive solution w1 to a certain scalar field equation. By utilizing the property of the positive solution w1, we can apply the general theory of Grillakis, Shatah and Strauss (1987) [11] and show the stability and instability of the standing wave.
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