Recent preprints.

My CV, with a complete publication list PDF format

An Introduction to KAM Theory PDF format

Counter-propagating wave on fluid surfaces and the continuum limit of the FPU model. PDF format.

Invariant manifolds and the long-time asymptotics of the Navier-Stokes and vorticity equations on $\real^2$. Postscript format or PDF format.

Long-time asymptotics of the Navier-Stokes and vorticity equations on $\real^3$. Postscript format or PDF format.

Reduced equations for models of laminated materials in thin domains. Postscript format or PDF format.

Higher order corrections to the KdV approximation for a Boussinesq equation. Postscript format or PDF format.

On the validity of 2D water wave models. Postscript format.

Propagation of ultra-short optical pulses in nonlinear media. PDF format.

Global stability of vortex solutions of the two-dimensional Navier-Stokes equation. Postscript format or PDF format.

Ultra-short pulses in linear and nonlinear media. Postscript format or PDF format.

Existence and stability of asymmetric Burgers vortices. PDF format.

Three-dimensional stability of Burgers vortices: the low Reynolds number case. PDF format.

Invariant Manifolds and the Stability of Traveling Waves in Scalar Viscous Conservation Laws. PDF format

Lectures on dynamical systems and partial differential equations with applications to the Navier-Stokes equations. PDF format.

Long tails in the long time asymptotics of quasi-linear hyperbolic-parabolic systems of conservation laws. PDF format

Generalized Helmholtz-Kirchoff model for two dimensional distributed vortex motion. PDF format

Outline and references for lectures on "Coherent Motions in the Fermi-Pasta-Ulam Model" delived at the Nantes Summer School on Hamiltonian Partial Differential Equations . PDF format

Counterpropagating two-soliton solutions in the FPU lattice. PDF format

Asymptotic two-soliton solutions solutions in the Fermi-Pasta-Ulam model. PDF format

Using global invariant manifolds to understand metastability in Burgers equation with small viscosity. PDF format

Asymptotic stabilty of the Toda m-soliton. PDF format

A multi-moment vortex method for 2D viscous fluids. PDF format

Justification of the NLS approximation for a quasilinear water wave model. PDF format (Correction to preceding manuscript: PDF format)

Relative equilibria of the (1+N)-vortex problem. PDF format

Metastability and rapid convergence to quasi-stationary bar states for the 2D Navier-Stokes equations. PDF format

Orbital stability of localized structures via Backlund transfomations. PDF format

Dissipative partial differential equations and dynamical systems. PDF format

Inverse spectral theory for uniformly open gaps in a weighted Sturm-Liouville problem. PDF format

Analysis of enhanced diffusion in Taylor dispersion via a model problem. PDF format

An explanation of metastability in the viscous Burgers equation with periodic boundary conditions via a spectral analysis. PDF format

Modified energy functionals and the NLS approximation. PDF format

Energy dissipation in Hamiltonian chains of rotators. PDF format

Breathers as metastable states for the discrete NLS equation. PDF format

Critical points of the Strichartz functional. PDF format

Vortices in stably-stratified rapidly rotating Boussinesq convection. PDF format

Rigorous justification of Taylor dispersion via center manifolds and hypocoercivity PDF format

Decay of Hamiltonian breathers under dissipation Open Access

Damped and driven breathers and metastability PDF format

Asymptotic approximation of a modified compressible Navier-Stokes sytem PDF format