Manuel del Pino - Departamento de Ingeniería Matemática and CMM, Universidad de Chile, Casilla 170 Correo 3, Santiago, Chile (email)
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.
operator, Toda system, Concentration phenomena, multiple transition
layers, positive Gauss curvature.
Received: March 2010; Revised: April 2010; Published: April 2010.
2013 IF (1 year).923