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 | |
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