77 citations · 260 across the 14 of their papers we have counts for
15 papers
Bifurcation analysis for axisymmetric capillary water waves with vorticity and swirl
André Erhardt, Erik Wahlén, Jörg Weber
We study steady axisymmetric water waves with general vorticity and swirl, subject to the influence of surface tension. This can be formulated as an elliptic free boundary problem…
Traveling water waves -- the ebb and flow of two centuries
Susanna V. Haziot, Vera Mikyoung Hur, Walter Strauss +4
This survey covers the mathematical theory of steady water waves with an emphasis on topics that are at the forefront of current research. These areas include: variational characte…
Global bifurcation of capillary-gravity water waves with overhanging profiles and arbitrary vorticity
Erik Wahlén, Jörg Weber
We study two-dimensional periodic capillary-gravity water waves propagating at the free surface of water in a flow with arbitrary, prescribed vorticity over a flat bed. Using confo…
Fully localised three-dimensional gravity-capillary solitary waves on water of infinite depth
Boris Buffoni, Mark D. Groves, Erik Wahlén
Fully localised solitary waves are travelling-wave solutions of the three-dimensional gravity-capillary water wave problem which decay to zero in every horizontal spatial direction…
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.…
On the stability of solitary water waves with a point vortex
Kristoffer Varholm, Erik Wahlén, Samuel Walsh
This paper investigates the stability of traveling wave solutions to the free boundary Euler equations with a submerged point vortex. We prove that sufficiently small-amplitude wav…
A variational principle for three-dimensional water waves over Beltrami flows
Evgeniy Lokharu, Erik Wahlén
We consider steady three-dimensional gravity-capillary water waves with vorticity propagating on water of finite depth. We prove a variational principle for doubly periodic waves w…
Steady three-dimensional rotational flows: an approach via two stream functions and Nash-Moser iteration
Boris Buffoni, Erik Wahlén
We consider the stationary flow of an inviscid and incompressible fluid of constant density in the region . We are concerned with flows that are period…
Variational existence theory for hydroelastic solitary waves
Mark D. Groves, Benedikt Hewer, Erik Wahlén
This paper presents an existence theory for solitary waves at the interface between a thin ice sheet (modelled using the Cosserat theory of hyperelastic shells) and an ideal fluid…
Transverse instability of periodic and generalized solitary waves for a fifth-order KP model
Mariana Haragus, Erik Wahlén
We consider a fifth-order Kadomtsev-Petviashvili equation which arises as a two-dimensional model in the classical water-wave problem. This equation possesses a family of generaliz…
On Whitham's conjecture of a highest cusped wave for a nonlocal dispersive equation
Mats Ehrnstrom, Erik Wahlén
We consider the Whitham equation , where L is the nonlocal Fourier multiplier operator given by the symbol . G. B. Whitham conjectur…
Periodic solitons for the elliptic-elliptic focussing Davey-Stewartson equations
Mark D. Groves, Shu-Ming Sun, Erik Wahlén
We consider the elliptic-elliptic, focussing Davey-Stewartson equations, which have an explicit bright line soliton solution. The existence of a family of periodic solitons, which…
On the existence and stability of solitary-wave solutions to a class of evolution equations of Whitham type
Mats Ehrnström, Mark D. Groves, Erik Wahlén
We consider a class of pseudodifferential evolution equations of the form in which is a linear smoothing operator and is at least quadratic nea…
Existence and conditional energetic stability of three-dimensional fully localised solitary gravity-capillary water waves
Boris Buffoni, Mark D. Groves, Shu-Ming Sun +1
In this paper we show that the hydrodynamic problem for three-dimensional water waves with strong surface-tension effects admits a fully localised solitary wave which decays to the…
Discrete wave turbulence of rotational capillary water waves
Adrian Constantin, Elena Kartashova, Erik Wahlén
We study the discrete wave turbulent regime of capillary water waves with constant non-zero vorticity. The explicit Hamiltonian formulation and the corresponding coupling coefficie…