On the stability of kink solutions of the $\Phi^4$ model in $1+1$ space time dimensions
On the stability of kink solutions of the $\Phi^4$ model in $1+1$ space time dimensions
A kink is a stationary solution to a cubic one dimensional wave equation $\bigl(\partial_t^2-\partial_x^2\bigr)\phi = \phi-\phi^3$ that has different limits when $x$ goes to $-\infty$ and $+\infty$, like $H(x) =\tanh(x/\sqrt{2})$. Asymptotic stability of this solution under small odd perturbation in the energy space has been studied in a recent work …