Waves in granular chains
 periodic and solitary waves in chains of beads, compactons
 stiff Newton's cradle : periodic waves, breathers and surface modes
 granular metamaterials with local resonators : bright and dark breathers
 longlived breathers
Modulation equations : derivation and dynamics
 discrete pSchrödinger equation
 logarithmic KdV equation
 from granular metamaterials to cubic NLS
 from diatomic FPU lattice to coupled (stationary) NLS equations
 Floquet spectrum for Rogue waves in NLS
 breathers and vortices in discrete cubic NLS
Waves in nonsmooth systems
 solitary waves and fronts in piecewiselinear discontinuous systems (McKean nonlinearity)
 timeperiodic oscillations in a chain of impact oscillators
Numerical computation of localized waves in nonlinear lattices
 solitary waves and fronts
 traveling breathers in a strongly nonlinear lattice with phase invariance
 traveling breathers in KleinGordon lattices
 breathers for fractionalorder nonlinearities and nonsmooth systems
 breathers for smooth nonlinearities
 dark breathers
 breathers in presence of lattice defects
 surface modes
 vortices in discrete cubic NLS
Networks near the anticontinuum (weak coupling) limit
 continuation from infinity for localized equilibria, breathers and solitary waves
 fronts in a bistable system
 timeperiodic oscillations in a chain of impact oscillators
 strongly nonlinear lattices, breathers and surface modes with superexponential decay
 vortices in discrete cubic NLS
 periodic and relative periodic orbits in Euclideaninvariant Hamiltonian systems
Existence/nonexistence theorems for
discrete breathers
 different types of localized oscillations : bright,
dark, periodic, longlived, traveling
 chains of oscillators
with local potentials
 networks of oscillators
with Euclidean invariance (including FPU)
 discrete nonlinear Schrödinger equations
Center manifold reduction in infinite dimensions
 center manifold theorems for infinitedimensional maps
 spatial dynamics for timeperiodic oscillations (bright and dark breathers) in lattices
 systems of advancedelay differential equations (solitary waves, fronts and traveling breathers in lattices)
 review on center manifolds for lattice differential equations
 quasilinear elliptic PDE with coefficients close to Dirac delta distributions
 DubreilJacotin  Long equation (semilinear elliptic PDE)
