48 citations · 207 across the 28 of their papers we have counts for
6 papers · 1 filter
Liouville chains: new hybrid vortex equilibria of the 2D Euler equation
Vikas S. Krishnamurthy, Miles H. Wheeler, Darren G. Crowdy +1
A large class of new exact solutions to the steady, incompressible Euler equation on the plane is presented. These hybrid solutions consist of a set of stationary point vortices em…
Global bifurcation of solitary waves for the Whitham equation
Tien Truong, Erik Wahlén, Miles H. Wheeler
The Whitham equation is a nonlocal shallow water-wave model which combines the quadratic nonlinearity of the KdV equation with the linear dispersion of the full water wave problem.…
Global bifurcation of anti-plane shear fronts
Robin Ming Chen, Samuel Walsh, Miles H. Wheeler
We consider anti-plane shear deformations of an incompressible elastic solid whose reference configuration is an infinite cylinder with a cross section that is unbounded in one dir…
Large-amplitude internal fronts in two-fluid systems
Robin Ming Chen, Samuel Walsh, Miles H. Wheeler
In this announcement, we report results on the existence of families of large-amplitude internal hydrodynamic bores. These are traveling front solutions of the full two-phase incom…
Global bifurcation for monotone fronts of elliptic equations
Robin Ming Chen, Samuel Walsh, Miles H. Wheeler
In this paper, we present two results on global continuation of monotone front-type solutions to elliptic PDEs posed on infinite cylinders. This is done under quite general assumpt…
Nonexistence of subcritical solitary waves
Vladimir Kozlov, Evgeniy Lokharu, Miles H. Wheeler
We prove the nonexistence of two-dimensional solitary gravity water waves with subcritical wave speeds and an arbitrary distribution of vorticity. This is a longstanding open probl…