# American Institute of Mathematical Sciences

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

## The Jacobi-Toda system and foliated interfaces

 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.
Citation: Manuel del Pino, Michal Kowalczyk, Juncheng Wei. The Jacobi-Toda system and foliated interfaces. Discrete & Continuous Dynamical Systems - A, 2010, 28 (3) : 975-1006. doi: 10.3934/dcds.2010.28.975
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