SNAKING IN THE SWIFT-HOHENBERG EQUATION
This final project will study the Swift–Hohenberg equation using cubic and quintic nonlinear part stable and unstable local solution with different lengths around the Maxwell point b etween spatial and periodic homogeous states. To find snaking in the Swift-Hohenberg equation obtained from the deriv...
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| Format: | Final Project |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/65453 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | This final project will study the Swift–Hohenberg equation using cubic and quintic nonlinear part stable and unstable local solution with different lengths around the Maxwell point b etween spatial and periodic homogeous states. To find snaking in the Swift-Hohenberg equation obtained from the derivative against time and space so that it will produce snaking. Herein, we focus on Swift-Hohenberg equation with cubic and quintic nonlinearity, obtained by discretizing the spatial derivatives of the Swift-Hohenberg equation using the central finite difference. In this final project will also be discussed a phenomenon called homoclinic snaking. This term refers to the back and forth oscillations in a branch of steady spatially localized states sometimes referred to as dissipative solitons that are found in partial differential equations of sufficiently high order in space exhibiting bistability between a spatially homogeneous and a spatially periodic state. Moreover, we also investigate further regarding the bifurcation structure of stationary localized patterns of the Swift–Hohenberg equation. Numerical bifurcation analysis will be carried out to find patterns in the one-dimensional Swift-Hohenberg equation with cubic-quintic nonlinearities. |
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