27 citations · 98 across the 12 of their papers we have counts for
12 papers
Solitary waves and vortices in a Nonlinear Schrödinger equation with ponderomotive nonlinearity
D. K. Campbell, J. Cuevas-Maraver, R. Goh +1
In the present work we revisit a ponderomotive nonlinearity model used to examine self-trapped laser beams in plasma. Upon briefly considering the exact stationary 1D solutions of…
Patterned fronts in the wake of a parameter ramp in the complex Ginzburg Landau equation
Ryan Goh, Benjamin Krewson, Nilay Patel +1
We study of the formation of pattern-forming fronts in the presence of a rigidly-propagating parameter ramp which is slowly-varying in space. In the context of the prototypical sup…
Pitchfork bifurcation along a slow parameter ramp: coherent structures in the critical scaling
Ryan Goh, Tasso J. Kaper, Arnd Scheel
We investigate the slow passage through a pitchfork bifurcation in a spatially extended system, when the onset of instability is slowly varying in space. We focus here on the criti…
Fronts in the wake of a parameter ramp: slow passage through pitchfork and fold bifurcations
Ryan Goh, Tasso J. Kaper, Arnd Scheel +1
This work studies front formation in the Allen-Cahn equation with a parameter heterogeneity which slowly varies in space. In particular, we consider a heterogeneity which mediates…
Strain and defects in oblique stripe growth
Kelly Chen, Zachary Deiman, Ryan Goh +2
We study stripe formation in two-dimensional systems under directional quenching in a phase-diffusion approximation including non-adiabatic boundary effects. We find stripe formati…
Delayed Hopf bifurcation and space-time buffer curves in the Complex Ginzburg-Landau equation
Ryan Goh, Tasso J. Kaper, Theodore Vo
In this article, the phenomenon of delayed Hopf bifurcations (DHB) in reaction-diffusion PDEs is analyzed in the cubic Complex Ginzburg-Landau equation with a slowly-varying parame…
Growing stripes, with and without wrinkles
M. Avery, R. Goh, O. Goodloe +2
We present results on stripe formation in the Swift-Hohenberg equation with a directional quenching term. Stripes are "grown" in the wake of a moving parameter step line, and we an…
Pattern-forming fronts in a Swift-Hohenberg equation with directional quenching - parallel and oblique stripes
Ryan Goh, Arnd Scheel
We study the effect of domain growth on the orientation of striped phases in a Swift-Hohenberg equation. Domain growth is encoded in a step-like parameter dependence that allows st…
Universal wavenumber selection laws in apical growth
Ryan Goh, Rajendra Beekie, Daniel Matthias +2
We study pattern-forming dissipative systems in growing domains. We characterize classes of boundary conditions that allow for defect-free growth and derive universal scaling laws…
Pattern formation in the wake of triggered pushed fronts
Ryan Goh, Arnd Scheel
Pattern-forming fronts are often controlled by an external stimulus which progresses through a stable medium at a fixed speed, rendering it unstable in its wake. By controlling the…
Hopf bifurcation from fronts in the Cahn-Hilliard equation
Ryan Goh, Arnd Scheel
We study Hopf bifurcation from traveling-front solutions in the Cahn-Hilliard equation. The primary front is induced by a moving source term. Models of this form have been used to…
Triggered Fronts in the Complex Ginzburg Landau Equation
Ryan Goh, Arnd Scheel
We study patterns that arise in the wake of an externally triggered, spatially propagating instability in the complex Ginzburg-Landau equation. We model the trigger by a spatial in…