ANALYSIS OF SNAKING SOLUTIONS IN DISCRETE ALLEN-CAHN EQUATIONS WITH CUBIC-QUINTIC AND CUBIC-QUINTIC-SEPTIC NONLINEARITY
In this thesis, a discrete Allen-Cahn model of equations with cubic-quintic nonlinearity will be compared with cubic-quintic-septic nonlinearity. This equation model combines bistability and bonding between sites or particles. Next, we will investigate the behavior of localized solutions that bif...
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| Format: | Theses |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/68347 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | In this thesis, a discrete Allen-Cahn model of equations with cubic-quintic nonlinearity
will be compared with cubic-quintic-septic nonlinearity. This equation
model combines bistability and bonding between sites or particles. Next, we will investigate
the behavior of localized solutions that bifurcate from uniform solutions.
The localized solution will form snaking in certain cases depending on the bifurcation
parameter. The effects of nonlinearity and coupling strength between sites
affect snaking behavior. The stronger the bond strength between sites, the smaller
the snaking that appears. Meanwhile, the greater the nonlinearity effect of the given
system, the greater the snaking that appears. This change in snaking behavior will
determine the area owned by the pinning region. The model with cubic-quinticseptic
nonlinearity will investigate the behavior of solutions and snaking for small,
medium, and large nonlinearity effects. By varying the values of the model parameters,
it will affect the stability of the solution and the snaking behavior. Furthermore,
it will also determine the minimum total potential of the system which is represented
by the maxwell point value. Maxwell point is a condition that satisfies when the
upper state and zero state are energetically equal. |
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