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July  2010, 28(3): 975-1006. doi: 10.3934/dcds.2010.28.975

The Jacobi-Toda system and foliated interfaces

Manuel del Pino 1, , Michal Kowalczyk 1, and  Juncheng Wei 2,

1. 

Departamento de Ingeniería Matemática and CMM, Universidad de Chile, Casilla 170 Correo 3, Santiago, Chile, Chile
2. 

Department of Mathematics, Chinese University of Hong Kong, Shatin, New Territories, Hong Kong

Received  March 2010 Revised  April 2010 Published  April 2010

Let (M ,ğ) be an $N$-dimensional smooth (compact or noncompact) Riemannian manifold. We introduce the elliptic Jacobi-Toda system on (M ,ğ). 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.
Keywords: Jacobi operator, positive Gauss curvature., Concentration phenomena, multiple transition layers, Toda system.
Mathematics Subject Classification: 35J60, 58J05, 58J37, 53C21, 53C2.
Citation: Manuel del Pino, Michal Kowalczyk, Juncheng Wei. The Jacobi-Toda system and foliated interfaces. Discrete & Continuous Dynamical Systems, 2010, 28 (3) : 975-1006. doi: 10.3934/dcds.2010.28.975
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