67 citations · 169 across the 13 of their papers we have counts for
8 papers · 1 filter
Turing and wave instabilities in hyperbolic reaction-diffusion systems: The role of second-order time derivatives and cross-diffusion terms on pattern formation
Joshua Ritchie, Andrew L. Krause, Robert A. Van Gorder
Hyperbolic reaction-diffusion equations have recently attracted attention both for their application to a variety of biological and chemical phenomena, and for their distinct featu…
Adiabatic soliton management: Controlling solitary wave motion while keeping the wave envelope unchanged
Robert A. Van Gorder
We describe how to control the motion -- both speed and propagation direction -- of a nonlinear traveling wave in real time via soliton management with time-varying dispersion/diff…
Unstaggered-staggered solitons on one- and two-dimensional two-component discrete nonlinear Schrödinger lattices
Robert A. Van Gorder, Andrew L. Krause, Boris A. Malomed +1
We study coupled unstaggered-staggered soliton pairs emergent from a system of two coupled discrete nonlinear Schrödinger (DNLS) equations with the self-attractive on-site self-pha…
Turing conditions for pattern forming systems on evolving manifolds
Robert A. Van Gorder, Václav Klika, Andrew L. Krause
The study of pattern-forming instabilities in reaction-diffusion systems on growing or otherwise time-dependent domains arises in a variety of settings, including applications in d…
Amplitude death criteria for coupled complex Ginzburg-Landau systems
Robert A. Van Gorder, Andrew L. Krause, James A. Kwiecinski
Amplitude death, which occurs in a system when one or more macroscopic wavefunctions collapse to zero, has been observed in mutually coupled solid-state lasers, analog circuits, an…
Coupled complex Ginzburg-Landau systems with saturable nonlinearity and asymmetric cross-phase modulation
Robert A. Van Gorder, Andrew L. Krause, Ferran Brosa Planella +1
We formulate and study dynamics from a complex Ginzburg-Landau system with saturable nonlinearity, including asymmetric cross-phase modulation (XPM) parameters. Such equations can…
Wave propagation across interfaces induced by different interaction exponents in ordered and disordered Hertz-like granular chains
Armin Kekić, Robert A. Van Gorder
We study solitary wave propagation in 1D granular crystals with Hertz-like interaction potentials. We consider interfaces between media with different exponents in the interaction…
Unstaggered-staggered solitons in two-component discrete nonlinear Schrödinger lattices
Boris A. Malomed, D. J. Kaup, Robert A. Van Gorder
We present stable bright solitons built of coupled unstaggered and staggered components in a symmetric system of two discrete nonlinear Schrödinger (DNLS) equations with the attrac…