Variational construction of basic heteroclinic solutions for an Allen-Cahn equation

TL;DR

This paper develops a variational method to construct minimal heteroclinic solutions for the Allen-Cahn equation, extending known results from rational to irrational rotation vectors.

Contribution

It introduces a variational approach to construct heteroclinic solutions for irrational rotation vectors in the Allen-Cahn equation, generalizing previous rational case results.

Findings

Constructed minimal heteroclinic solutions for irrational rotation vectors.

Extended the theory from rational to irrational cases.

Provided a variational framework applicable to these solutions.

Abstract

We establish a variational construction of minimal and without self-intersection solutions for an Allen-Cahn equation, especially for those corresponding to irrational rotation vectors. These consequences generalize the results of rational cases of Rabinowitz and Stredulinsky to irrational cases.