Symmetry of Traveling Wave Solutions to the Allen-Cahn Equation in $\Er^2$
Changfeng Gui
TL;DR
This paper proves that monotone traveling wave solutions to the balanced Allen-Cahn equation in two dimensions are symmetric, and discusses related results for the unbalanced case, advancing understanding of solution structures.
Contribution
It establishes the symmetry of monotone traveling wave solutions for the balanced Allen-Cahn equation in the plane, a new result in the study of these solutions.
Findings
Monotone traveling waves are symmetric in the balanced case.
Discussion of symmetry properties in the unbalanced Allen-Cahn equation.
Provides mathematical proof of symmetry in two-dimensional solutions.
Abstract
In this paper, we prove even symmetry of monotone traveling wave solutions to the balanced Allen-Cahn equation in the entire plane. Related results for the unbalanced Allen-Cahn equation are also discussed.
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