SNAKING PHENOMENON ON CHECKERBOARD LATTICE - Daniel, Juan
We present a study of time-independent solutions of the two-dimensional discrete Allen–Cahn equation with cubic and quintic nonlinearity. In this paper, we will consider using checkerboard lattice. The equation admits uniform and localised states. We can obtain localised solutions by combining two different states of uniform solutions, which can develop a snaking structure in the bifurcation diagrams. We find that the complexity and width of the snaking diagrams depend on the number of ‘patch interfaces’ admitted by the lattice systems. We will also compare the snaking solutions obtained from the one-dimensional lattice and the two-dimensional lattice.