Cnoidal waves for the quintic Klein-Gordon and Schrödinger equations: Existence and orbital instability

Published 24 Mar 2022 in math.AP | (2203.13002v1)

Abstract: In the present paper, we establish the existence and orbital instability results of cnoidal periodic waves for the quintic Klein-Gordon and nonlinear Schr\"odinger equations. The spectral analysis for the corresponding linearized operator is established by using the Floquet theory. The orbital instability is determined by applying an abstract result due to Shatah and Strauss.

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