$\phi^4$ equation

Mathematical Analysis of Fractal Kink-Antikink Collisions in the $\varphi^4$ Model featured image
Solitary wave collisions

Mathematical Analysis of Fractal Kink-Antikink Collisions in the $\varphi^4$ Model

We analyze the fractal structure seen in kink-antikink collisions of the $\varphi^4$ equation. The analysis is based on qualitative ordinary differential equation models related to …

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Roy Goodman
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Kink-antikink collisions in the $\phi^4$ equation: The $n$-bounce resonance and the separatrix map featured image
$\phi^4$ equation

Kink-antikink collisions in the $\phi^4$ equation: The $n$-bounce resonance and the separatrix map

We provide a detailed mathematical explanation of a phenomenon known as the two-bounce resonance observed in collisions between kink and anti-kink traveling waves of the phi-four …

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Roy Goodman
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