77 citations · 218 across the 12 of their papers we have counts for
13 papers · 1 filter
A resonant Lyapunov centre theorem with an application to doubly periodic travelling hydroelastic waves
Rami Ahmad, Mark David Groves, Dag Nilsson
We present a Lyapunov centre theorem for an antisymplectically reversible Hamiltonian system exhibiting a nondegenerate or semisimple resonance as a detuning parameter…
Analytical Study of a generalised Dirichlet-Neumann operator and application to three-dimensional water waves on Beltrami flows
Mark D. Groves, Dag Nilsson, Stefano Pasquali +1
In this paper we consider three-dimensional steady water waves with vorticity, under the action of gravity and surface tension; in particular we consider so-called Beltrami flows,…
Existence of Davey--Stewartson type solitary waves for the fully dispersive Kadomtsev--Petviashvilii equation
Mats Ehrnström, Mark D. Groves, Dag Nilsson
We prove existence of small-amplitude modulated solitary waves for the full-dispersion Kadomtsev--Petviashvilii (FDKP) equation with weak surface tension. The resulting waves are s…
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…
Small-amplitude fully localised solitary waves for the full-dispersion Kadomtsev--Petviashvili equation
Mats Ehrnström, Mark Groves
The KP-I equation \[ (u_t-2uu_x+\tfrac{1}{2}(β-\tfrac{1}{3})u_{xxx})_x -u_{yy}=0 \] arises as a weakly nonlinear model equation for gravity-capillary waves with strong surface tens…
Spatial dynamics methods for solitary waves on a ferrofluid jet
Mark Groves, Dag Nilsson
This paper presents existence theories for several families of axisymmetric solitary waves on the surface of an otherwise cylindrical ferrofluid jet surrounding a stationary metal…
Pattern formation on the free surface of a ferrofluid: spatial dynamics and homoclinic bifurcation
Mark D. Groves, David J. B. Lloyd, Athanasios Stylianou
We establish the existence of spatially localised one-dimensional free surfaces of a ferrofluid near onset of the Rosensweig instability, assuming a general (nonlinear) magnetisati…
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…
A variational reduction and the existence of a fully-localised solitary wave for the three-dimensional water-wave problem with weak surface tension
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…
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…
A dimension-breaking phenomenon for water waves with weak surface tension
Mark D. Groves, Shu-Ming Sun, Erik Wahlén
It is well known that the water-wave problem with weak surface tension has small-amplitude line solitary-wave solutions which to leading order are described by the nonlinear Schröd…
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…