Compacton formation under Allen--Cahn dynamics
Emilio N.M. Cirillo, Nicoletta Ianiro, Giulio Sciarra
TL;DR
This paper investigates the formation of compactons in a generalized Allen-Cahn equation with variable higher order stiffness, providing analytical solutions for stationary states and numerical analysis of their dynamics.
Contribution
It introduces a new class of solutions called compactons in the Allen-Cahn framework, with analytical derivations and numerical simulations demonstrating their formation.
Findings
Existence of compacton solutions between phases.
Analytical stationary solutions derived.
Numerical simulations confirm compacton formation.
Abstract
We study the solutions of a generalized Allen-Cahn equation deduced from a Landau energy functional, endowed with a non-constant higher order stiffness. We analytically solve the stationary problem and deduce the existence of so-called compactons, namely, connections on a finite interval between the two phases. The dynamics problem is numerically solved and compacton formation is described.
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