SNAKING PHENOMENON ON CHECKERBOARD LATTICE
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 tw...
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| Format: | Final Project |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/68401 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | 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. |
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