The stability of nonlinear waves has a distinguished history and an abundance of richly
structured yet accessible examples, which makes it not only an important subject but also an …

We present an analytical study of the Fermi–Pasta–Ulam (FPU) α–model with periodic
boundary conditions. We analyze the dynamics corresponding to initial data with one low …

A review is given of the works on the FPU problem that were particularly relevant in
connection with the metastability perspective, proposed in the year 1982. The idea is that …

In this paper we construct and approximate breathers in the DNLS model starting from the
continuous limit: such periodic solutions are obtained as perturbations of the ground state of …

We address the problem of equipartition in a long Fermi–Pasta–Ulam (FPU) chain. After
giving a precise relation between FPU and Korteweg–de Vries we use the latter equation to …

Using Lie group theory and canonical transformations, we construct explicit solutions of
nonlinear Schrodinger equations with spatially inhomogeneous nonlinearities. We present …

We study analytically the dynamics of two-dimensional rectangular lattices with periodic
boundary conditions. We consider anisotropic initial data supported on one low-frequency …

We use the Galerkin averaging method to construct a coordinate transformation putting a
nonlinear PDE in Poincaré normal form up to finite order. We also give a rigorous estimate of …

We study the dispersive evolution of modulated pulses in a nonlinear oscillator chain
embedded in a background field. The atoms of the chain interact pairwise with an arbitrary …

Standing waves are a fundamental class of solutions of nonlinear wave equations with a
spatial reflection symmetry, and they routinely arise in optical and oceanographic …