The Jacobi-Toda system and foliated interfaces

Manuel Del Pino, Michal Kowalczyk, Juncheng Wei

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)

Abstract

Let (M, g̃) be an N-dimensional smooth (compact or noncompact) Riemannian manifold. We introduce the elliptic Jacobi-Toda systemon (M,g̃)-We review various recent results on its role in the construction of solutions with multiple interfaces of the Allen-Cahn equation on compact manifolds and entire space, as well as multiple-front traveling waves for its parabolic counterpart.

Original languageEnglish
Pages (from-to)975-1006
Number of pages32
JournalDiscrete and Continuous Dynamical Systems
Volume28
Issue number3
DOIs
Publication statusPublished - 1 Nov 2010

Keywords

  • Concentration phenomena
  • Jacobi operator
  • Multiple transition layers
  • Positive Gauss curvature
  • Toda system

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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