Traveling wave solutions for bistable fractional Allen-Cahn equations with a pyramidal front

Hardy Chan, Juncheng Wei

Using the method of sub-super-solution, we construct a solution of $(-\Delta {)}^{s}u-c{u}_z-f(u)=0$ on ${\mathbb{R}}^3$ of pyramidal shape. Here $(-\Delta {)}^s$ is the fractional Laplacian of sub-critical ord…