Kink stability in nonlinear Klein-Gordon equations

December 10, 2021
Nonlinear Klein-Gordon equations whose potential have a double well admit kink solutions (most famous examples: Phi4, Sine-Gordon). I will present joint work with Fabio Pusateri which establishes the stability of this kink under some spectral conditions on the linearized problem. The key idea of the proof is to view the problem through the distorted Fourier transform associated with the linearized problem.