相关论文: Peakons arising as particle paths beneath small-am…

In the limit of small values of the aspect ratio parameter (or wave steepness) which measures the amplitude of a surface wave in units of its wave-length, a model equation is derived from the Euler system in infinite depth (deep water)…

We establish the existence of small-amplitude uni- and bimodal steady periodic gravity waves with an affine vorticity distribution, using a bifurcation argument that differs slightly from earlier theory. The solutions describe waves with…

In this paper we construct periodic capillarity-gravity water waves with a piecewise constant vorticity distribution. They describe water waves traveling on superposed linearly sheared currents that have different vorticities. This is…

We investigate the particle trajectories in an irrotational shallow water flow over a flat bed as periodic waves propagate on the water's free surface. Within the linear water wave theory, we show that there are no closed orbits for the…

We present a large-amplitude existence theory for two-dimensional solitary waves propagating through a two layer body of water. The domain of the fluid is bounded below by an impermeable flat ocean floor and above by a free boundary at…

This article is meant as an accessible introduction to/tutorial on the analytical construction and numerical simulation of a class of non-standard solitary waves termed \emph{peakompactons}. These peaked compactly supported waves arise as…

The dynamics of small, yet heavy, identical particles in turbulence exhibits singularities, called caustics, that lead to large fluctuations in the spatial particle-number density, and in collision velocities. For large particle, inertia…

Optical vortices arise as phase singularities of the light fields and are of central interest in modern optical physics. In this paper, some existence theorems are established for stationary vortex wave solutions of a general class of…

The basic building blocks of many forms of optical topologies are particle-like singularities in phase and polarisation, giving rise to lines of darkness that weave complex threads in 3D space. Although known for half a century since…

This paper studies periodic traveling gravity waves at the free surface of water in a flow of constant vorticity over a flat bed. Using conformal mappings the free-boundary problem is transformed into a quasilinear pseudodifferential…

We determine the phase portrait of a Hamiltonian system of equations describing the motion of the particles in linear deep-water waves. The particles experience in each period a forward drift which decreases with greater depth.

We consider a family of Stokes waves on vorticity flow parameterized by a parameter. For large value of the parameter the Stokes waves approach the Stokes extreme wave. We prove that there are infinitely many subharmonic bifurcation points…

In this paper we examine the flow generated by coupled surface and internal small-amplitude water waves in a two-fluid layer model, where we take the upper layer to be rotational (constant vorticity) and the lower layer to be irrotational.…

This paper considers two-dimensional steady solitary waves with constant vorticity propagating under the influence of gravity over an impermeable flat bed. Unlike in previous works on solitary waves, we allow for both internal stagnation…

Optical vortices are phase singularities nested in electromagnetic waves that constitute a fascinating source of phenomena in the physics of light and display deep similarities to their close relatives, quantized vortices in superfluids and…

We investigate regular configurations of a small number of particles settling under gravity in a viscous fluid. The particles do not touch each other and can move relative to each other. The dynamics is analyzed in the point-particle…

We prove local higher-order asymptotics for extreme water waves with vorticity near stagnation points. We obtain that the behaviour of solutions and their regularity depend substantially on the vorticity. In particular, we show that extreme…

In this paper, we establish the existence of Stokes waves with piecewise smooth vorticity in a two-dimensional, infinitely deep fluid domain. These waves represent traveling water waves propagating over sheared currents in a semi-infinite…

Wave-packet interference is investigated within the complex quantum Hamilton-Jacobi formalism using a hydrodynamic description. Quantum interference leads to the formation of the topological structure of quantum caves in space-time Argand…

We study wave-current interactions in two-dimensional water flows of constant vorticity over a flat bed. For large-amplitude periodic traveling waves that propagate at the water surface in the same direction as the underlying current…