2020/06/01 by Fábio Natali, Natali, Fábio, Guilherme de Loreno +1
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics #Nonlinear Photonic Systems
paper · pdf · doi:10.48550/arxiv.2006.01305
openalex publication_date 2020/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we establish the existence and stability properties of odd periodic waves related to the Klein-Gordon type equations, which include the well known ϕ4 and ϕ6 models. Existence of periodic waves is determined by using a general planar theory of ODE. The spectral analysis for the corresponding linearized operator is established using the monotonicity of the period map combined with an improvement of the standard Floquet theory. Orbital stability in the odd sector of the energy space is proved using exclusively the monotonicity of the period map. The orbital instability of explicit solutions for the ϕ4 and ϕ6 models is presented using the abstract approach in \citegrillakis1.