1 citations · 1 across the 8 of their papers we have counts for
8 papers
Surface Wave Solutions in 1D and 2D for the Broer-Kaup-Boussinesq-Kupershmidt (BKBK) System
Darryl D. Holm, Ruiao Hu, Hanchun Wang
The BKBK system is a singular perturbation of the classical shallow water equations which modifies their transport velocity to depend on wave elevation slope. This modification int…
Compound Burgers-KdV Soliton Behaviour: Refraction, Reflection and Fusion
Darryl D. Holm, Ruiao Hu, Oliver D. Street +1
We consider a coupled PDE system between the Burgers equation and the KdV equation to model the interactions between `bore'-like structures and wave-like solitons in shallow water.…
Plasma dynamics in thin domains
Darryl D. Holm, Ruiao Hu, Oliver D. Street
In the present work, we study the geometric structures of the Rotating Shallow Water Magnetohydrodynamics (RSW-MHD) equations through a Lie group invariant Euler-Poincaré variation…
Stochastic multisymplectic PDEs and their structure-preserving numerical methods
Ruiao Hu, Linyu Peng
We construct stochastic multisymplectic systems by considering a stochastic extension to the variational formulation of multisymplectic partial differential equations proposed in […
Collisions of Burgers Bores with Nonlinear Waves
Albert. Dombret, Darryl D. Holm, Ruiao Hu +2
This paper treats nonlinear wave current interactions in their simplest form, as an overtaking collision. In one spatial dimension, the paper investigates the collision interaction…
Deterministic and Stochastic Geometric Mechanics for Hall MHD
Darryl D. Holm, Ruiao Hu, Oliver D. Street
We derive new models of stochastic Hall magnetohydrodynamics (MHD) by using a symmetry-reduced stochastic Euler-Poincaré variational principle. The new stochastic Hall MHD theory h…
Geometric theory of perturbation dynamics around non-equilibrium fluid flows
Darryl D. Holm, Ruiao Hu, Oliver D. Street
The present work investigates the evolution of linear perturbations of time-dependent ideal fluid flows with advected quantities, expressed in terms of the second order variations…
Geometric Mechanics of the Vertical Slice Model
Darryl D. Holm, Ruiao Hu, Oliver D. Street
The goals of the present work are to: (i) investigate the dynamics of oceanic frontogenesis by taking advantage of the geometric mechanics underlying the class of Vertical Slice Mo…