The Jacobi-Toda system  and  foliated interfaces

Manuel del Pino; Michal Kowalczyk; Juncheng Wei

doi:10.3934/dcds.2010.28.975

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2010, Volume 28, Issue 3: 975-1006. Doi: 10.3934/dcds.2010.28.975

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The Jacobi-Toda system and foliated interfaces

1.
Departamento de Ingeniería Matemática and CMM, Universidad de Chile, Casilla 170 Correo 3, Santiago
2.
Department of Mathematics, Chinese University of Hong Kong, Shatin, New Territories, Hong Kong

Received: February 28, 2010

Revised: March 31, 2010

Published: August 2010

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Abstract

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.

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Mathematics Subject Classification: 35J60, 58J05, 58J37, 53C21, 53C22.

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