7 papers
Compressible steady water waves
Abba Ramadan, Samuel Walsh
In this paper, we consider the existence of small- and large-amplitude compressible water waves. These are solutions of the two-dimensional free boundary isentropic Euler equations…
Minimizers for the Cahn-Hilliard energy functional with the Flory-Huggins potential under strong anchoring conditions
Shibin Dai, Abba Ramadan, Natasha Sharma
In this paper, we theoretically and numerically study the minimizers for the Cahn-Hilliard energy with the Flory-Huggins potential under the strong anchoring condition, i.e., the D…
Curve Lengthening Bifurcations in Modally Filtered Nonlinear Schrödinger Systems
Keith Promislow, Abba Ramadan
Extensions of the parametric nonlinear Schrödinger equations (PNLS) for phase-sensitive optical resonance are developed that preserve the curve lengthening bifurcation seen in the…
Curvature and Chaos in the Defocusing Parameteric Nonlinear Schrodinger System
Keith Promislow, Abba Ramadan
The parametric nonlinear Schrodinger equation models a variety of parametrically forced and damped dispersive waves. For the defocusing regime, we derive a normal velocity for the…
On the stability of solitary waves in the NLS system of the third-harmonic generation
Abba Ramadan, Atanas G. Stefanov
We consider the NLS system of the third-harmonic generation, which was introduced by Sammut. Our interest is in solitary wave solutions and their stability properties. The recent w…
On the stability of the compacton waves for the degenerate KdV and NLS models
Sevdzhan Hakkaev, Abba Ramadan, Atanas G. Stefanov
In this paper, we consider the degenerate semi-linear Schrödinger and Korteweg-deVries equations in one spatial dimension. We construct special solutions of the two models, namely…
On the standing waves of the Schroedinger equation with concentrated nonlinearity
Abba Ramadan, Atanas G. Stefanov
We study the concentrated NLS on , with power non-linearities, driven by the fractional Laplacian, . We construct the solitary waves explicitl…