Nonlinear Dynamics

Finite and infinite dimensional systems

Hamiltonian systems

Canonical Perturbation Theory and Lie Transforms

Chaotic dynamics

Action diffusion

Bifurcation theory

Melnikov theory

Lattices and chains of coupled oscillators

Nonlinear wave equations

Wave propagation in inhomogeneous nonlinear media

Nonlinear wave-particle interactions and Applications to Plasma Physics and Microwave Sources

Nonlinear theory of wave-particle interactions

Collective particle behavior

Electron/Ion cyclotron heating and current drive

Complex electron dynamics in gyrotron resonators

Nonlinear wave propagation

Turbulence and transport

Nonlinear Wave Propagation and Applications to Optical Communications

Spatial and temporal wave localization

Solitons and Inverse Scattering Transform

Lattice Solitons and Nonlinear Waveguide Arrays

Soliton perturbation theories

Effective particle approaches

Soliton Communications (temporal solitons)

All-optical signal processing devices (spatial solitons)

Dynamically induced photonic structures in optical media

Analytical and numerical methods

     Perturbation methods

     Numerical integration of ODEs and PDEs

     Spectral methods