39 citations · 162 across the 16 of their papers we have counts for
16 papers
Relational space-time and de Broglie waves
Tony Lyons
Relative motion of particles is examined in the context of relational space-time. It is shown that de Broglie waves may be derived as a representation of the coordinate maps betwee…
On the intrinsic wave-particle duality of coordinate maps
Tony Lyons
The relative motion of material, point-like observers is analysed in terms of coordinate maps between the respective rest-frame of each observer. Under the assumption these maps ar…
Particle paths in equatorial flows
Tony Lyons
We investigate particle trajectories in equatorial flows with geophysical corrections caused by the earth's rotation. Particle trajectories in the flows are constructed using pairs…
Variable eddy viscosities in the atmospheric boundary layer from ageostrophic wind-speed profiles
Tony Lyons
We generate explicit height-dependent eddy viscosity coefficients in the Ekman layer from convex wind speed profiles. The solutions we obtain are parameterized in terms of the rela…
Geophysical internal equatorial waves of extreme form
Tony Lyons
The existence of internal geophysical waves of extreme form is confirmed and an explicit solution presented. The flow is confined to a layer lying above an eastward current while t…
Camassa-Holm cuspons, solitons and their interactions via the dressing method
Rossen Ivanov, Tony Lyons, Nigel Orr
A dressing method is applied to a matrix Lax pair for the Camassa-Holm equation, thereby allowing for the construction of several global solutions of the system. In particular solu…
The dynamic pressure in deep-water extreme Stokes waves
Tony Lyons
In this paper we consider the dynamic pressure in a deep-water extreme Stokes wave. While the presence of stagnation points introduces a number of mathematical complications, maxim…
Solitons of shallow-water models from energy-dependent spectral problems
Jack Haberlin, Tony Lyons
The current work investigates the soliton solutions of the Kaup-Boussinesq equation using the Inverse Scattering Transform method. We outline the construction of the Riemann-Hilber…
A dressing method for soliton solutions of the Camassa-Holm equation
Rossen Ivanov, Tony Lyons, Nigel Orr
The soliton solutions of the Camassa-Holm equation are derived by the implementation of the dressing method. The form of the one and two soliton solutions coincides with the form o…
The pressure distribution in extreme Stokes waves
Tony Lyons
In this paper we prove that the pressure beneath an extreme Stokes wave over finite depth is strictly increasing with depth. Additionally it is shown that the pressure decreases in…
The pressure in a deep-water Stokes wave of greatest height
Tony Lyons
In this paper we investigate the qualitative behaviour of the pressure function beneath an extreme Stokes wave over infinite depth. The presence of a stagnation point at the wave-c…
Two-component higher order Camassa-Holm systems with fractional inertia operator: a geometric approach
Joachim Escher, Tony Lyons
In the following we study the qualitative properties of solutions to the geodesic flow induced by a higher order two-component Camassa-Holm system. In particular, criteria to ensur…
Two-component equations modelling water waves with constant vorticity
Joachim Escher, David Henry, Boris Kolev +1
In this paper we derive a two-component system of nonlinear equations which model two-dimensional shallow water waves with constant vorticity. Then we prove well-posedness of this…
Integrable models for shallow water with energy dependent spectral problems
Rossen I. Ivanov, Tony Lyons
We study the inverse problem for the so-called operators with energy depending potentials. In particular, we study spectral operators with quadratic dependance on the spectral para…
The 2-component dispersionless Burgers equation arising in the modelling of blood flow
Tony Lyons
This article investigates the properties of the solutions of the dispersionless two-component Burgers (B2) equation, derived as a model for blood-flow in arteries with elastic wall…
Dark solitons of the Qiao's hierarchy
Rossen Ivanov, Tony Lyons
We obtain a class of soliton solutions of the integrable hierarchy which has been put forward in a series of works by Z. Qiao. The soliton solutions are in the class of real functi…