Mathematics

A kink solution is an explicit stationary solution to the nonlinear wave equation equation $(\partial_t^2-\partial_x^2)\phi = \phi - \phi^3$ in one space dimension. We consider a small perturbation of this stationary solution, smooth and decaying at infinity. We obtain explicit rates of decay of that perturbed solution for large times that are $O(\epsilon^{-4})$, where $\epsilon$ is the size of the initial data. This is joint work with Nader Masmoudi.