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math.AP2026
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…
math.AP2026
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…
math.AP2026
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…