Index of research topics

(publications accessible through the links below)

    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)