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High-Frequency Instabilities of a Boussinesq-Whitham System: A Perturbative Approach
Ryan Creedon, Bernard Deconinck, Olga Trichtchenko
We analyze the spectral stability of small-amplitude, periodic, traveling-wave solutions of a Boussinesq-Whitham system. These solutions are shown numerically to exhibit high-frequ…
High-Frequency Instabilities of the Kawahara Equation: A Perturbative Approach
Ryan Creedon, Bernard Deconinck, Olga Trichtchenko
We analyze the spectral stability of small-amplitude, periodic, traveling-wave solutions of the Kawahara equation. These solutions exhibit high-frequency instabilities when subject…
Direct Characterization of Spectral Stability of Small Amplitude Periodic Waves in Scalar Hamiltonian Problems Via Dispersion Relation
Richard Kollár, Bernard Deconinck, Olga Trichtchenko
Various approaches to studying the stability of solutions of nonlinear PDEs lead to explicit formulae determining the stability or instability of the wave for a wide range of class…
A method for identifying stability regimes using roots of a reduced-order polynomial
Olga Trichtchenko
For dispersive Hamiltonian partial differential equations of order 2N+1, N integer, there are two criteria to analyse to examine the stability of small-amplitude, periodic travelli…
Stability of Periodic Travelling Flexural-Gravity Waves in Two Dimensions
Olga Trichtchenko, Paul Milewski, Emilian Parau +1
In this work, we solve the Euler's equations for periodic waves travelling under a sheet of ice using a reformulation introduced in Ablowitz et al. (2006). These waves are referred…
High-frequency instabilities of small-amplitude solutions of Hamiltonian PDEs
Bernard Deconinck, Olga Trichtchenko
Generalizing ideas of MacKay, and MacKay and Saffman, a necessary condition for the presence of high-frequency ( i.e., not modulational) instabilities of small-amplitude periodic s…