I am a professor in the Department of Mathematical Sciences at NJIT. My research applies methods of dynamical systems to (conservative, dispersive) nonlinear wave equations arising, for example, in optics and fluid mechanics. I am interested in dynamical and bifurcation phenomena, and I use techniques from Hamiltonian mechanics and perturbation theory, as well as extensive computations. My current research in vortex dynamics is supported by the NSF under DMS-2206016.
I led the effort to start the SIAM New York-New Jersey-Pennsylvania Section (SIAM NNP) and was its first president in 2023-2024. I have handed over the reins to a new leadership group.
Interests
- Nonlinear Waves
- Dynamical Systems
- Asymptotics and Perturbation Methods
- Scientific Computing
- Point Vortices
Education
- PhD, Mathematical Sciences, 1999New York University
- BS, Mathematics, 1994University of Michigan
Latest
- Phase portraits and the bifurcation set for the three-vortex interaction system
- Small-Mass Asymptotics of Massive Point Vortex Dynamics in Bose--Einstein Condensates I: Averaging and Normal Forms
- QGLAB: A MATLAB Package for Computations on Quantum Graphs
- A new canonical reduction of three-vortex motion and its application to vortex-dipole scattering
- An English Translation of Gröbli's Ph.D. Dissertation: "Specielle Probleme über die Bewegung geradliniger paralleler Wirbelfäden"
- SIAM New York – New Jersey – Pennsylvania Section Holds Inaugural Conference
- Efficient Manipulation of Bose-Einstein Condensates in a Double-Well Potential
- Apodizer Design to Efficiently Couple Light into a Fiber Bragg Grating
- Transition to instability of the leapfrogging vortex quartet
- An Optimal Control Approach to Gradient-Index Design for Beam Reshaping
- A Reduction-Based Strategy for Optimal Control of Bose-Einstein Condensates
- How should we LaTeX?
- Solitary Waves in Mass-in-Mass Lattices
- Loss of Physical Reversibility in Reversible Systems
- Transfer entropy for network reconstruction in a simple dynamical model
- In Memoriam: Richard Haberman
- Stability of Leapfrogging Vortex Pairs: A Semi-analytic Approach
- Topological features determining the error in the inference of networks using transfer entropy
- Drift of spectrally stable shifted states on star graphs
- Four Decades of Kink Interactions in Nonlinear Klein-Gordon Models: A Crucial Typo, Recent Developments and the Challenges Ahead
- Markdown: A Writing Tool for Every Applied Mathematician's Toolbox
- NLS bifurcations on the bowtie combinatorial graph and the dumbbell metric graph
- Mathematical Analysis of Fractal Kink-Antikink Collisions in the $\varphi^4$ Model
- Book Review, Methods of Mathematical Modeling by Witelski and Bowen
- What do I do with all these numerical simulations?
- Bifurcations of relative periodic orbits in NLS/GP with a triple-well potential
- Complex Behavior in Coupled Nonlinear Waveguides
- Self-trapping and Josephson tunneling solutions to the nonlinear Schrödinger / Gross-Pitaevskii Equation
- Dynamics of vortex dipoles in anisotropic Bose-Einstein condensates
- A Mechanical Analog of the Two-Bounce Resonance of Solitary Waves: Modeling and Experiment
- High-order Adaptive Method for Computing Two-dimensional Invariant Manifolds of Maps
- High-Order Bisection Method for Computing Invariant Manifolds of Two-Dimensional Maps
- Hamiltonian Hopf bifurcations and dynamics of NLS/GP standing-wave modes
- Nonlinear hydrodynamic phenomena in Stokes flow regime
- Stability and instability of nonlinear defect states in the coupled mode equations---analytical and numerical study
- Hysteretic and chaotic dynamics of viscous drops in creeping flows with rotation
- Chaotic scattering in solitary wave interactions: A singular iterated-map description
- Chaotic Scattering and the $n$-bounce Resonance in Solitary Wave Interactions
- Vector soliton interactions in birefringent optical fibers
- Trapping light with grating defects
- Kink-antikink collisions in the $\phi^4$ equation: The $n$-bounce resonance and the separatrix map
- Strong NLS soliton--defect interactions
- Interaction of sine-Gordon kinks with defects: The two-bounce resonance
- Trapping of kinks and solitons by defects: phase space transport in finite-dimensional models
- Stopping Light on a Defect
- Modulations in the leading edges of midlatitude storm tracks
- Interaction of sine-Gordon kinks with defects: phase space transport in a two-mode model
- Nonlinear propagation of light in one-dimensional periodic structures
- Trigger Waves in a Model for Catalysis