On $1$d quadratic Klein-Gordon equations with a potential and symmetries

Abstract

This paper is a continuation of a previous work Germain-Pusateri (2020) by the first two authors. We focus on $1$ dimensional quadratic Klein-Gordon equations with a potential, under some assumptions that are less general than Germain-Pusateri (2020), but allow us to present some simplifications in the proof of global existence with decay for small solutions. In particular, we can propagate a stronger control on a basic $L^2$-weighted type norm while providing some shorter and less technical proofs for some of the arguments.

References in corpus (1)

• Nonexistence of small, odd breathers for a class of nonlinear wave equations

Cited by in corpus (2)

• Asymptotic stability near the soliton for quartic Klein-Gordon in 1D
• Techniques for Solving Static Klein-Gordon Equation with Self-Interaction $\lambda {\varphi }^4$ and Arbitrary Spherical Source Terms