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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id-itb.:684012022-09-15T07:47:38ZSNAKING PHENOMENON ON CHECKERBOARD LATTICE Daniel, Juan Indonesia Final Project homoclinic snaking, discrete Allen–Cahn equation, bistable systems, localised structures, checkerboard lattice. INSTITUT TEKNOLOGI BANDUNG https://digilib.itb.ac.id/gdl/view/68401 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. text |
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Institut Teknologi Bandung |
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Institut Teknologi Bandung Library |
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Indonesia Indonesia |
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Indonesia |
| description |
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. |
| format |
Final Project |
| author |
Daniel, Juan |
| spellingShingle |
Daniel, Juan SNAKING PHENOMENON ON CHECKERBOARD LATTICE |
| author_facet |
Daniel, Juan |
| author_sort |
Daniel, Juan |
| title |
SNAKING PHENOMENON ON CHECKERBOARD LATTICE |
| title_short |
SNAKING PHENOMENON ON CHECKERBOARD LATTICE |
| title_full |
SNAKING PHENOMENON ON CHECKERBOARD LATTICE |
| title_fullStr |
SNAKING PHENOMENON ON CHECKERBOARD LATTICE |
| title_full_unstemmed |
SNAKING PHENOMENON ON CHECKERBOARD LATTICE |
| title_sort |
snaking phenomenon on checkerboard lattice |
| url |
https://digilib.itb.ac.id/gdl/view/68401 |
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1822933633618411520 |