Related papers: Explicit multi-slit Loewner flows and their geomet…
A new important relation between fluid mechanics and differential geometry is established. We study smooth steady solutions to the Euler equations with the additional property: the velocity vector is orthogonal to the gradient of the…
In this note, we study the integrability of geodesic flow in the background of a very general class of spacetimes with NUT-charge(s) in higher dimensions. This broad set encompasses multiply NUT-charged solutions, electrically and…
The radial Komatu-Loewner equation is a differential equation for certain normalized conformal mappings that can be used to describe the growth of slits within multiply connected domains. We show that it is possible to choose constant…
Multisymplectic geometry is an adequate formalism to geometrically describe first order classical field theories. The De Donder-Weyl equations are treated in the framework of multisymplectic geometry, solutions are identified as integral…
We first prove stochastic representation formulae for space-time harmonic mappings defined on manifolds with evolving Riemannian metric. We then apply these formulae to derive Liouville type theorems under appropriate curvature conditions.…
We consider the Loewner differential equation generating univalent maps of the unit disk (or of the upper half-plane) onto itself minus a single slit. We prove that the circular slits, tangent to the real axis are generated by H\"older…
We investigated the analytical solution of fractional order K(m,n) type equation with variable coefficient which is an extended type of KdV equations into a genuinely nonlinear dispersion regime. By using the Lie symmetry analysis, we…
We study the magnetic geodesic flows on 2-surfaces having an additional first integral which is independent of the Hamiltonian at a fixed energy level. The following two cases are considered: when there exists a quadratic in momenta…
We review works on the asymptotic stability of the Couette flow. The majority of the paper is aimed towards a wide range of applied mathematicians with an additional section aimed towards experts in the mathematical analysis of PDEs.
The left-invariant sub-Riemannian problem on the group of motions of a plane is considered. Sub-Riemannian geodesics are parametrized by Jacobi's functions. Discrete symmetries of the problem generated by reflections of pendulum are…
The present letter obtains the exact solution and geometric phase of the time-dependent Schr\"{o}dinger equation governing the dipole oscillator in the exterior electric field, by making use of the Lewis-Riesenfeld invariant theory and the…
We formulate the mapping between a large class of nonlinear wave equations and flow equations for barotropic fluid with internal surface tension and capillary effects. Motivated by statistical mechanics and multi-channel physics arguments,…
We study multifractal spectra of the geodesic flows on rank 1 surfaces without focal points. We compute the entropy of the level sets for the Lyapunov exponents and estimate its Hausdorff dimension from below. In doing so, we employ and…
As is widely recognized in Lyapunov analysis, linearized Hamilton's equations of motion have two marginal directions for which the Lyapunov exponents vanish. Those directions are the tangent one to a Hamiltonian flow and the gradient one of…
Poincar\'e recognized that phase portraits are mainly structured around fixed points. Nevertheless, the knowledge of fixed points and their properties is not sufficient to determine the whole structure of chaotic attractors. In order to…
Over the last two decades, lattice Boltzmann methods have become an increasingly popular tool to compute the flow in complex geometries such as porous media. In addition to single phase simulations allowing, for example, a precise…
We obtain the full equations of motion for a wide, pivoted, slider bearing. These are used to review the choice of the optimal position for the pivot point, to discuss its response to time-dependent sliding velocity, and to determine the…
The problem of computing differential constraints for a family of evolution PDEs is discussed from a constructive point of view. A new method, based on the existence of generalized characteristics for evolution vector fields, is proposed in…
This paper introduces the geometry of the open string Floer theory of gauged Landau-Ginzburg model via gauged Witten equations. Given a $G$-invariant Morse-Bott holomorphic function $W$ on a Hamiltonian space $(M,\omega,G),$ Lefschetz…
In this paper we state the variational principle for the weighted porous media equation. It extends V.I. Arnold's approach to the description of Euler flows as a geodesics on some manifold, i.e. as a critical points of some energy…