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math.AP2026
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,…
math.AP2024
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,…