Abstract
We analyze solutions of the \(\phi ^4\) model in 2 and 3 spatial dimensions. For infinite domains, the solutions are of the bubble type, they collapse in finite time and give rise to transient waves. In inhomogeneous waveguides with Neumann boundary conditions, kinks will accelerate for narrowing widths and can be reflected if they do not have enough energy to cross the defect. In the presence of dissipation, kinks propagate at a constant radial speed. Dissipative kinks will travel in a smooth waveguide but can be trapped by sharp enlargements.
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The author thanks the CRIANN computing center for the use of its facilities.
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Caputo, JG. (2019). The \(\phi ^4\) Model in Higher Dimensions. In: Kevrekidis, P., Cuevas-Maraver, J. (eds) A Dynamical Perspective on the ɸ4 Model. Nonlinear Systems and Complexity, vol 26. Springer, Cham. https://doi.org/10.1007/978-3-030-11839-6_11
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DOI: https://doi.org/10.1007/978-3-030-11839-6_11
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