30 citations · 63 across the 10 of their papers we have counts for
11 papers
Modulation leading to frequency downshifting of water waves in the vicinity of the Benjamin-Feir transition
Daniel J. Ratliff, Olga Trichtchenko, Thomas J. Bridges
For Stokes waves in finite depth within the neighbourhood of the Benjamin-Feir stability transition, there are two families of periodic waves, one modulationally unstable and the o…
A Novel Method for Generating 3D Hydrodynamic Conservation Laws
James Wing Chee Graham, Katie L Oliveras, Olga Trichtchenko
We extend the recent work of Oliveras arXiv:2008.00940 and Oliveras & Calatola-Young arXiv:2105.07580 to develop a new nonlocal formulation of the water-wave problem for a three-di…
High-Frequency Instabilities of Stokes Waves
Ryan Creedon, Bernard Deconinck, Olga Trichtchenko
Euler's equations govern the behavior of gravity waves on the surface of an incompressible, inviscid, and irrotational fluid of arbitrary depth. We investigate the spectral stabili…
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…