Article Contents
Article Contents

# The Jacobi-Toda system and foliated interfaces

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

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