Stability and instability of standing-wave solutions to one dimensional quadratic-cubic Klein-Gordon equations

2022/09/09 by Daniele Garrisi, Garrisi, Daniele
Engineering · Mathematics · #35Q55 #47J35 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #Functional Analysis (math.FA) #Numerical methods for differential equations #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2209.04158

openalex publication_date 2022/09/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the stability of standing-waves solutions to a scalar non-linear Klein-Gordon equation in dimension one with a quadratic-cubic non-linearity. Orbits are obtained by applying the semigroup generated by the negative complex unit multiplication on a critical point of the energy constrained to the charge.

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