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Helmholtz's equations provide the motion of a system of N vortices which describes a planar incompressible fluid with zero viscosity. A relative equilibrium is a particular solution of these equations for which the distances between the…
We obtain a new exact solution to the field equations in the EGB modified theory of gravity for a 5-dimensional spherically symmetric static distribution. By using a transformation, the study is reduced to the analysis of a single second…
Some systems were recently put forth by Nguyen et. al. as models for studying the interaction of long and short waves in dispersive media. These systems were shown to possess synchronized Jacobi elliptic solutions as well as synchronized…
An explicit formula for the interaction energy of $n$ vortices in the abelian Higgs (or Ginzburg-Landau) model is derived, valid in the regime where all vortices are close to one another. An immediate consequence of this formula is that the…
We elaborate a theory of giant vortices [1] based on an asymptotic expansion in inverse powers of their winding number $n$. The theory is applied to the analysis of vortex solutions in the abelian Higgs (Ginzburg-Landau) model. Specific…
The theory of vortex motion in a dilute superfluid of inhomogeneous density demands a boundary layer approach, in which different approximation schemes are employed close to and far from the vortex, and their results matched smoothly…
A particular solution to the equations of motion of the Abelian Higgs model is given. The solution involves the Jacobi elliptic functions as well as the Heun functions.
We first reformulate and expand with several novel findings some of the basic results in the integrability of Abel equations. Next, these results are applied to Vein's Abel equation whose solutions are expressed in terms of the third order…
It is shown that dynamics of the interface between ideal fluid and light viscous fluid is exactly integrable in the approximation of small surface slopes for two-dimensional flow. Stokes flow of viscous fluid provides a relation between…
We consider the motion of a rigid body immersed in an ideal flow occupying the plane, with bounded initial vorticity. In that case there exists a unique corresponding solution which is global in time, in the spirit of the famous work by…
In this paper, we consider a moving rigid solid immersed in a potential fluid. The fluid-solid system fills the whole two dimensional space and the fluid is assumed to be at rest at infinity. Our aim is to study the inverse problem,…
We consider the inviscid limit for the two-dimensional incompressible Navier-Stokes equation in the particular case where the initial flow is a finite collection of point vortices. We suppose that the initial positions and the circulations…
We consider a new partial differential equation, of a similar form to the Camassa-Holm shallow water wave equation, which was recently obtained by Degasperis and Procesi using the method of asymptotic integrability. We prove the exact…
We investigate the interior Einstein's equations in the case of a static, axially symmetric, perfect fluid source. We present a particular line element that is specially suitable for the investigation of this type of interior gravitational…
The dynamics of a circular thin vortex ring and a sphere moving along the symmetry axis of the ring in an inviscid incompressible fluid is studied on the basis of Euler's equations of motion. The equations of motion for position and radius…
We consider the motion of several rigid bodies immersed in a two-dimensional incompress-ible perfect fluid, the whole system being bounded by an external impermeable fixed boundary. The fluid motion is described by the incompressible Euler…
An analytic method to calculate the vortex number on a torus is constructed, focusing on analytic vortex solutions to the Chern-Simons-Higgs theory, whose governing equation is the so-called Jackiw-Pi equation. The equation is one of the…
This investigation deals with some exact solutions of the equations governing the steady plane motions of an incompressible third grade fluid by using complex variables and complex functions. Some of the solutions admit, as particular…
The point vortex system is usually considered as an idealized model where the vorticity of an ideal incompressible two-dimensional fluid is concentrated in a finite number of moving points. In the case of a single vortex in an otherwise…
We formulate a solution to the Algebraic version of the Inverse Jacobi problem. Using this solution we produce explicit addition laws on any algebraic curve generalizing the law suggested by Leykin [2] in the case of (n, s) curves. This…