We describe a simple mechanical system, a ball rolling along a specially-designed landscape, that mimics the dynamics of a well known phenomenon, the two-bounce resonance of …
An efficient and accurate numerical method is presented for computing invariant manifolds of maps which arise in the study of dynamical systems. A quasi-interpolation method due to …
We describe an efficient and accurate numerical method for computing smooth approximations to invariant manifolds of planar maps, based on geometric modeling ideas from Computer …
We examine the dynamics of solutions to nonlinear Schrödinger/Gross-- Pitaevskii equations that arise due to semisimple indefinite Hamiltonian Hopf bifurcations---the collision of …
We investigate nonlinear phenomena in dispersed two-phase systems under creeping-flow conditions. We consider nonlinear evolution of a single deformed drop and collective dynamics …
Coupled backward and forward wave amplitudes of an electromagnetic field propagating in a periodic and nonlinear medium at Bragg resonance are governed by the nonlinear coupled …
We investigate nonlinear phenomena in dispersed two-phase systems under creeping-flow conditions. We consider nonlinear evolution of a single deformed drop and collective dynamics …
We derive a family of singular iterated maps---closely related to Poincaré maps---that describe chaotic interactions between colliding solitary waves. The chaotic behavior of such …
We present a new and complete analysis of the n-bounce resonance and chaotic scattering in solitary wave collisions. In these phenomena, the speed at which a wave exits a collision …
We consider the interactions of two identical, orthogonally polarized vector solitons in a nonlinear optical fiber with two polarization directions, described by a coupled pair of …