Related papers: Isotropic curve flows on $R^{n+1, n}$
The signature transform, defined by the formal tensor series of global iterated path integrals, is a homomorphism between the path space and the tensor algebra that has been studied in geometry, control theory, number theory as well as…
We formulate an isoperimetric deformation of curves on the Minkowski plane, which is governed by the defocusing mKdV equation. Two classes of exact solutions to the defocusing mKdV equation are also presented in terms of the $\tau$…
We give the following results for Pinkall's central affine curve flow on the plane: (i) a systematic and simple way to construct the known higher commuting curve flows, conservation laws, and a bi-Hamiltonian structure, (ii) Baecklund…
For any arbitrary algebraic curve, we define an infinite sequence of invariants. We study their properties, in particular their variation under a variation of the curve, and their modular properties. We also study their limits when the…
We construct a sequence of commuting central affine curve flows on $R^n\backslash 0$ invariant under the action of $SL(n,R)$ and prove the following results: (a) The central affine curvatures of a solution of the j-th central affine curve…
We show that stable localized topological soliton textures (skyrmions) with $\pi_2$ topological charge $\nu \geq 1$ exist in a classical 2D Heisenberg model of a ferromagnet with uniaxial anisotropy. For this model the soliton exist only if…
We propose a consistent setup for a holographic dual of Bjorken flow of strongly coupled large-Nc N=4 SYM-theory plasma. We employ Eddington-Finkelstein type coordinates for the dual geometry, and we propose a late-time expansion there. We…
Isomorphs are curves in the thermodynamic phase diagram of invariant excess entropy, structure, and dynamics, while pseudoisomorphs are curves of invariant structure and dynamics, but not of the excess entropy. The latter curves have been…
We analyze the behavior of an isentropic gas in a narrow pipe with periodically-varying cross-sectional area. Using multiple-scale perturbation theory, we derive homogenized effective equations, which take the form of a constant-coefficient…
We discuss the topology of the parameter space of invertible phases with an onsite symmetry $G$, i.e., quantum many-body ground states that have neither fractionalization nor spontaneous breaking of the symmetry. The classification of…
The problem of kink stability of isothermal spherical self-similar flow in newtonian gravity is revisited. Using distribution theory we first develop a general formula of perturbations, linear or non-linear, which consists of three sets of…
In this note, our aim is to show that families of smooth hypersurfaces of $\mathbb R^{n+1}$ which are all $C^1$--close enough to a fixed compact, embedded one, have uniformly bounded constants in some relevant inequalities for mathematical…
In this paper, we study the isotropy group of Lotka-Volterra derivations of $K[x_{1},\cdots,x_{n}]$, i.e., a derivation $d$ of the form $d(x_{i})=x_{i}(x_{i-1}-C_{i}x_{i+1})$. If $n=3$ or $n \geq 5$, we have shown that the isotropy group of…
We argue that an arbitrary general relativistic static anisotropic fluid sphere, (static and spherically symmetric but with transverse pressure not equal to radial pressure), can nevertheless be successfully mimicked by suitable linear…
In this short note, we consider self-similar immersions $F: \mathbb{R}^n \to \mathbb{R}^{n+k}$ of the Graphic Mean Curvature Flow of higher co-dimension. We show that the following is true: Let $F(x) = (x,f(x)), x \in \mathbb{R}^{n}$ be a…
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…
We build an example of a non-transitive, dynamically coherent partially hyperbolic diffeomorphism $f$ on a closed $3$-manifold with exponential growth in its fundamental group such that $f^n$ is not isotopic to the identity for all $n\neq…
The theory of soliton gas had been previously developed for unidirectional integrable dispersive hydrodynamics in which the soliton gas properties are determined by the overtaking elastic pairwise interactions between solitons. In this…
In this paper, we consider the evolution of spacelike graphic curves defined over a piece of hyperbola $\mathscr{H}^{1}(1)$, of center at origin and radius $1$, in the $2$ dimensional Lorentz-Minkowski plane $\mathbb{R}^{2}_{1}$ along an…
It is well-known that a function on an open set in $\mathbb R^d$ is smooth if and only if it is arc-smooth, i.e., its composites with all smooth curves are smooth. In recent work, we extended this and related results (for instance, a real…