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

• DOI: 10.1016/j.jmaa.2022.126203
• Publication Date: 2022-03-25T17:05:15Z
• Authors: Gabriel E. Bitten...; Guilherme de Loreno
• Keywords: Quintic function; Floquet theory; Operator (biology); Klein–Gordon equation

20 pages, 5 figures. To appear in Journal of Mathematical Analysis and Applications<br/>In the present paper, we establish the existence and orbital instability results of cnoidal periodic waves for the quintic Klein-Gordon and nonlinear Schr��dinger 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.<br/>