Publications

We show via analytical perturbation theory that the leapfrogging vortex quartet becomes unstable exactly at the critical ratio $\alpha= \phi^{-2}.$

We use an optimal control framework to efficiently couple light into a fiber Bragg grating, improving a previously-reported 66 percent transmission to 88 percent.

We use optimal control based on a Galerkin-truncated model to transfer a BEC from one well of a two-well potential to the other.

Applications of Bose-Einstein Condensates (BEC) often require that the condensate be prepared in a specific complex state. Optimal …

We address the problem of reshaping light in the Schrödinger optics regime from the perspective of optimal control theory. In …

We consider the existence of spatially localized traveling wave solutions of the mass-in-mass lattice. Under an anti-resonance …

A dynamical system is said to be reversible if, given an output, the input can always be recovered in a well-posed manner. …

We investigate the stability of a one-parameter family of periodic solutions of the four-vortex problem known as leapfrogging orbits. …

When the coefficients of the cubic terms match the coefficients in the boundary conditions at a vertex of a star graph and satisfy a …

The problem of inferring interactions from observations of individual behavior in networked dynamical systems is ubiquitous in science …

We analyze the fractal structure seen in kink-antikink collisions of the $\varphi^4$ equation. The analysis is based on qualitative …

We consider the bifurcations of standing wave solutions to the nonlinear Schrödinger equation (NLS) posed on a quantum graph consisting …

The nonlinear Schrödinger/Gross–Pitaevskii (NLS/GP) equation is considered in the presence of three equally-spaced potentials. …

We describe a simple mechanical system, a ball rolling along a specially-designed landscape, that mimics the dynamics of a well known …

We study the motion of a vortex dipole in a Bose-Einstein condensate confined to an anisotropic trap. We focus on a system of ordinary …

We study the long-time behavior of solutions to the nonlinear Schrödinger / Gross-Pitaevskii equation (NLS/GP) with a symmetric …

An efficient and accurate numerical method is presented for computing invariant manifolds of maps which arise in the study of dynamical …

We examine the dynamics of solutions to nonlinear Schrödinger/Gross– Pitaevskii equations that arise due to semisimple indefinite …

We describe an efficient and accurate numerical method for computing smooth approximations to invariant manifolds of planar maps, based …

We investigate nonlinear phenomena in dispersed two-phase systems under creeping-flow conditions. We consider nonlinear evolution of a …

We derive a family of singular iterated maps—closely related to Poincaré maps—that describe chaotic interactions between …

We investigate nonlinear phenomena in dispersed two-phase systems under creeping-flow conditions. We consider nonlinear evolution of a …

Coupled backward and forward wave amplitudes of an electromagnetic field propagating in a periodic and nonlinear medium at Bragg …

We present a new and complete analysis of the n-bounce resonance and chaotic scattering in solitary wave collisions. In these …

We provide a detailed mathematical explanation of a phenomenon known as the two-bounce resonance observed in collisions between kink …

Gap solitons are localized traveling waves that exist in Bragg grating optical fibers. We demonstrate a family of grating defects that …

We consider the interactions of two identical, orthogonally polarized vector solitons in a nonlinear optical fiber with two …

A model of soliton–defect interactions in the sine-Gordon equations is studied using singular perturbation theory. Melnikov …

We consider the interaction of a nonlinear Schrödinger soliton with a spatially localized (point) defect in the medium through which it …

We study a model derived by Fei et al. [Phys. Rev. A 45 (1992) 6019] of a kink solution to the sine-Gordon equation interacting with an …

Gap solitons are localized nonlinear coherent states that have been shown both theoretically and experimentally to propagate in …

We study models of Fei et al. and of Forinash et al of kinks in the sine-Gordon equation, and solitons in the nonlinear Schrodinger …

Downstream development is a term encompassinga variety of effects relating to the propagation of storm systems at midlatitude. We …

We consider the nonlinear propagation of light in an optical fiber waveguide as modeled by the anharmonic Maxwell-Lorentz equations …

We consider the model of catalysis due to Ziff, Gulari, and Barshad [Phys Rev. Lett. 56, 2553 (1986)] as a pattern formation problem. …