Kink dynamics in the 𝜙⁴ model: Asymptotic stability for odd perturbations in the energy space

We consider a classical equation known as the ϕ 4 \phi ^4 model in one space dimension. The kink, defined by H ( x ) = tanh ⁡ ( x / 2 ) H(x)=\tanh (x/{\sqrt {2}}) , is an explicit stationary solution of this model. From a result of Henry, Perez and Wreszinski it is known that the kink is orbitally s... View More