In this paper, we explore the metastable states of nonlinear Klein-Gordon equations with potentials. These states come from instability of a bound state under a nonlinear Fermi’s golden rule. In , Soffer and Weinstein studied the instability mechanism and obtained an anomalously slow-decaying rate 1/(1 + t) 41 . Here we develop a new method to study the evolution of L2 x norm of solutions to Klein-Gordon equations. With this method, we prove a H1 scattering result for Klein-Gordon equations with metastable states. By exploring the oscillations, with a dynamical system approach we also find a more robust and more intuitive way to derive the sharp decay rate 1/(1 + t) 14 .
|Original language||English (US)|
|Number of pages||43|
|Journal||Discrete and Continuous Dynamical Systems- Series A|
|State||Published - 2020|
All Science Journal Classification (ASJC) codes
- Discrete Mathematics and Combinatorics
- Applied Mathematics
- And phrases. Nonlinear Klein-Gordon equation
- Fermi’s golden rule
- Metastable states
- scattering scattering.