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
- long-lived breathers
Modulation equations : derivation and dynamics
- discrete p-Schrödinger 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 piecewise-linear discontinuous systems (McKean nonlinearity)
- time-periodic 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 Klein-Gordon lattices
- breathers for fractional-order 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
- time-periodic 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 Euclidean-invariant Hamiltonian systems
Existence/nonexistence theorems for
discrete breathers
- different types of localized oscillations : bright,
dark, periodic, long-lived, 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 infinite-dimensional maps
- spatial dynamics for time-periodic oscillations (bright and dark breathers) in lattices
- systems of advance-delay 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
- Dubreil-Jacotin - Long equation (semilinear elliptic PDE)
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