相关论文: Integrable negative flows of the Heisenberg ferrom…

Binary Bargmann symmetry constraints are applied to decompose soliton equations into finite-dimensional Liouville integrable Hamiltonian systems, generated from so-called constrained flows. The resulting constraints on the potentials of…

Two integrable $U(1)$-invariant peakon equations are derived from the NLS hierarchy through the tri-Hamiltonian splitting method. A Lax pair, a recursion operator, a bi-Hamiltonian formulation, and a hierarchy of symmetries and conservation…

We construct weak solutions of the anisotropic inverse mean curvature flow (A-IMCF) under very mild assumptions both on the anisotropy (which is simply a norm in $\mathbb R^N$ with no ellip\-ticity nor smoothness requirements, in order to…

Two integrable differential-difference equations are derived from a (2+1)-dimensional modified Heisenberg ferromagnetic equation and a resonant nonlinear Schr\"oinger equation respectively. Multi-soliton solutions of the resulted…

In this study, we investigate two distinct classes of normal geodesic flows associated with the left-invariant sub-Riemannian metric on the (2n + 1)-dimensional Heisenberg group. The first class arises from the left-invariant distribution,…

The reductions of the integrable N-wave type equations solvable by the inverse scattering method with the generalized Zakharov-Shabat systems L and related to some simple Lie algebra g are analyzed. The Zakharov- Shabat dressing method is…

Rotationally symmetric bodies with longitudinal cross sections of parabolic shape are frequently used to model astrophysical objects, such as magnetospheres and other blunt objects, immersed in interplanetary or interstellar gas or plasma…

We discuss the presence of exotic electromagnetic phenomena in systems with finite charge density which are described by hydrodynamics. We show that such systems generically have negative refractive index for low frequency electromagnetic…

This paper addresses the issue of the formulation of weak solutions to systems of nonlinear hyperbolic conservation laws as integral balance laws. The basic idea is that the "meaningful objects" are the fluxes, evaluated across domain…

We show the complete integrability and the existence of optical solitons of higher order nonlinear Schrodinger equation by inverse scattering method for a wide range of values of coefficients. This is achieved first by invoking a novel…

A deformation parameter of a bihamiltonian structure of hydrodynamic type is shown to parameterize different extensions of the AKNS hierarchy to include negative flows. This construction establishes a purely algebraic link between, on the…

We propose a systematic method to generalize the integrable Rosochatius deformations for finite dimensional integrable Hamiltonian systems to integrable Rosochatius deformations for infinite dimensional integrable equations. Infinite number…

The relationship between the compressible magnetohydrodynamic flows with low Mach number and the incompressible magnetohydrodynamic flows is investigated. More precisely, the convergence of weak solutions of the compressible isentropic…

This is a review of the main ideas of the inverse scattering method (ISM) for solving nonlinear evolution equations (NLEE), known as soliton equations. As a basic tool we use the fundamental analytic solutions (FAS) of the Lax operator L.…

In this paper we study the geodesic flow on nilmanifolds equipped with a left-invariant metric. We write the underlying definitions and find general formulas for the Poisson involution. As an example we develop the Heisenberg Lie group…

Direct numerical simulations of a liquid metal filling the gap between two concentric spheres are presented. The flow is governed by the interplay between the rotation of the inner sphere (measured by the Reynolds number Re) and a weak…

The dynamics of short intense electromagnetic pulses propagating in a relativistic pair plasma with small temperature asymmetry is of current interest. Such pulses were shown to be governed by a nonlinear Schrodinger equation with a new…

We study the propagation of low frequency shallow water waves on a one dimensional flow of varying depth. When taking into account dispersive effects, the linear propagation of long wavelength modes on uneven bottoms excites new solutions…

Isospectral flows are abundant in mathematical physics; the rigid body, the the Toda lattice, the Brockett flow, the Heisenberg spin chain, and point vortex dynamics, to mention but a few. Their connection on the one hand with integrable…

Using bidifferential calculus, we derive a vectorial binary Darboux transformation for an integrable matrix version of the first negative flow of the Kaup-Newell hierarchy. A reduction from the latter system to an integrable matrix version…