The Jacobi-Toda system and foliated interfaces

Manuel Del Pino; Michal Kowalczyk; Juncheng Wei

doi:10.3934/dcds.2010.28.975

The Jacobi-Toda system and foliated interfaces

Manuel Del Pino, Michal Kowalczyk, Juncheng Wei

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

11 Citations (SciVal)

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 language	English
Pages (from-to)	975-1006
Number of pages	32
Journal	Discrete and Continuous Dynamical Systems
Volume	28
Issue number	3
DOIs	https://doi.org/10.3934/dcds.2010.28.975
Publication status	Published - 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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10.3934/dcds.2010.28.975

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The Jacobi-Toda system and foliated interfaces

Abstract

Keywords

ASJC Scopus subject areas

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