4 papers
The Benjamin-Feir instability in KdV-like equations with general dispersion and monomial nonlinearity
Bhavna Kaushik, Bernard Deconinck
Nonlinear waves in dispersive media can be succeptible to modulational instabilities. We examine a category of scalar equations, with general dispersion and monomial nonlinearity,…
Stokes Waves in Water of Finite Depth
Eleanor Byrnes, Bernard Deconinck, Anastassiya Semenova
Periodic water waves of permanent form traveling at constant speed, the so-called Stokes waves, are studied in water of fixed finite depth using methods previously used in water of…
The explicit solution of linear, dissipative, second-order initial-boundary value problems with variable coefficients
Matthew Farkas, Bernard Deconinck
We derive explicit solution representations for linear, dissipative, second-order Initial-Boundary Value Problems (IBVPs) with coefficients that are spatially varying, with linear,…
Self-similarity and recurrence in stability spectra of near-extreme Stokes waves
Bernard Deconinck, Sergey A. Dyachenko, Anastassiya Semenova
We consider steady surface waves in an infinitely deep two--dimensional ideal fluid with potential flow, focusing on high-amplitude waves near the steepest wave with a 120 degree c…