Title: Nanopteron solutions of diatomic Fermi-Pasta-Ulam-Tsingou lattices with small mass-ratio,
Abstract: Consider an infinite chain of masses, each connected to its nearest neighbors
by a (nonlinear) spring. This is a Fermi-Pasta-Ulam-Tsingou lattice. We prove
the existence of traveling waves in the setting where the masses alternate in
size. In particular we address the limit where the mass ratio tends to zero.
The problem is inherently singular and we find that the traveling waves are not
true solitary waves but rather "nanopterons", which is to say, waves which
asymptotic at spatial infinity to very small amplitude periodic waves.
Moreover, we can only find solutions when the mass ratio lies in a certain open
set. The difficulties in the problem all revolve around understanding Jost
solutions of a nonlocal Schrödinger operator in its semi-classical limit.