116 citations · 406 across the 19 of their papers we have counts for
6 papers · 1 filter
The Kawahara Equation: Traveling Wave Solutions Joining Periodic Waves
Patrick Sprenger, Thomas J. Bridges, Michael Shearer
The Kawahara equation is a weakly nonlinear long-wave model of dispersive waves that emerges when leading order dispersive effects are in balance with the next order correction. Tr…
Dispersive Riemann problem for the Benjamin-Bona-Mahony equation
T. Congy, G. A. El, M. A. Hoefer +1
Long time dynamics of the smoothed step initial value problem or dispersive Riemann problem for the Benjamin-Bona-Mahony (BBM) equation are studied using asy…
Nonlinear Schrödinger equations and the universal description of dispersive shock wave structure
T. Congy, G. A. El, M. A. Hoefer +1
The nonlinear Schrödinger (NLS) equation and the Whitham modulation equations both describe slowly varying, locally periodic nonlinear wavetrains, albeit in differing amplitude-fre…
Stationary Expansion Shocks for a Regularized Boussinesq System
G. A. El, M. A. Hoefer, M. Shearer
Stationary expansion shocks have been recently identified as a new type of solution to hyperbolic conservation laws regularized by non-local dispersive terms that naturally arise i…
Expansion shock waves in regularised shallow water theory
Gennady A. El, Mark A. Hoefer, Michael Shearer
We identify a new type of shock wave by constructing a stationary expansion shock solution of a class of regularised shallow water equations that include the Benjamin-Bona-Mahoney…
Dispersive and diffusive-dispersive shock waves for nonconvex conservation laws
G. A. El, M. A. Hoefer, M. Shearer
We consider two physically and mathematically distinct regularization mechanisms of scalar hyperbolic conservation laws. When the flux is convex, the combination of diffusion and d…