JournalsaihpcVol. 39, No. 4pp. 905–926

Traveling wave solutions to the Allen–Cahn equation

  • Chao-Nien Chen

    National Tsing Hua University, Hsinchu, Taiwan

  • Vittorio Coti Zelati

    Università degli Studi di Napoli Federico II, Italy
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Abstract

For the Allen–Cahn equation, it is well known that there is a monotone standing wave joining the balanced wells of the potential. In this paper we study the existence of traveling wave solutions for the Allen–Cahn equation on an infinite channel. Such traveling wave solutions possess a large number of oscillations and they are obtained with the aid of variational arguments.

Cite this article

Chao-Nien Chen, Vittorio Coti Zelati, Traveling wave solutions to the Allen–Cahn equation. Ann. Inst. H. Poincaré Anal. Non Linéaire 39 (2022), no. 4, pp. 905–926

DOI 10.4171/AIHPC/23