Related papers: Geometric aspects of two- and threepeakons
We obtain estimates of the multiplicative constants appearing in local convergence results of the Riemannian Gauss-Newton method for least squares problems on manifolds and relate them to the geometric condition number of [P. B\"urgisser…
A survey of some recent and important results which have to do with integrable equations and their relationship with the theory of surfaces is given. Some new results are also presented. The concept of the moving frame is examined, and it…
We study the classical mechanics and dynamics of particles that retains some memory of quantum statistics. Our work builds on earlier work on the statistical mechanics and thermodynamics of such particles. Starting from the effective…
Consider briefly the equations of fluid dynamics-they describe the enormous wealth of detail in all the interacting physical elements of a fluid flow-whereas in applications we want to deal with a description of just that which is…
In this paper, we study orbital stability of peakons for the generalized modified Camassa-Holm (gmCH) equation, which is a natural higher-order generalization of the modified Camassa-Holm (mCH) equation, and admits Hamiltonian form and…
3-quasi-Sasakian manifolds were studied systematically by the authors in a recent paper as a suitable setting unifying 3-Sasakian and 3-cosymplectic geometries. This paper throws new light on their geometric structure which reveals to be…
Geometry of hypersurfaces defined by the relation which generalizes classical formula for free energy in terms of microstates is studied. Induced metric, Riemann curvature tensor, Gauss-Kronecker curvature and associated entropy are…
The recently developed 3D graphic statics (3DGS) lacks a rigorous mathematical definition relating the geometrical and topological properties of the reciprocal polyhedral diagrams as well as a precise method for the geometric construction…
Recently Vladimir Novikov found a new integrable analogue of the Camassa-Holm equation, admitting peaked soliton (peakon) solutions, which has nonlinear terms that are cubic, rather than quadratic. In this paper, the explicit formulas for…
We obtain general results on the dynamics of exactly conical geometries, where we use the notion of boundaries at infinity to characterize asymptotic behavior. As we demonstrate in examples, these notions also apply to smooth geometries…
In the dynamical triangulation model of 4D euclidean quantum gravity we measure two-point functions of the scalar curvature as a function of the geodesic distance. To get the correlations it turns out that we need to subtract a squared…
We describe how geometrical methods can be applied to a system with explicitly time-dependent second-class constraints so as to cast it in Hamiltonian form on its physical phase space. Examples of particular interest are systems which…
This paper is dedicated to provide theta function representations of algebro-geometric solutions and related crucial quantities for the two-component Camassa-Holm Dym (CHD2) hierarchy. Our main tools include the polynomial recursive…
We construct examples of 2-step Carnot groups related to quaternions and study their fine structure and geometric properties. This involves the Hamiltonian formalism, which is used to obtain explicit equations for geodesics and the…
We extend to the context of hyperbolic 3-manifolds with geodesic boundary Thurston's approach to hyperbolization by means of geometric triangulations. In particular, we introduce moduli for (partially) truncated hyperbolic tetrahedra, and…
Dynamics of sine-Gordon kinks in the presence of rapidly varying periodic perturbations of different physical origins is described analytically and numerically. The analytical approach is based on asymptotic expansions, and it allows to…
In this Letter the main steps in the inverse spectral construction of a family of non-smooth solitons (peakons) to the modified Camassa-Holm equation are oulined. It is shown that the inverse problem is solvable in terms of multi-point…
In this paper we introduce a two-component system, depending on a parameter $b$, which generalises the Camassa-Holm ($b=1$) and Novikov equations ($b=2$). By investigating its Lie algebra of classical and higher symmetries up to order $3$,…
In this article we study two related models of quantum geometry: generic random trees and two-dimensional causal triangulations. The Hausdorff and spectral dimensions that arise in these models are calculated and their relationship with the…
We investigate geometric properties of surfaces given by certain formulae. In particular, we calculate the singular curvature and the limiting normal curvature of such surfaces along the set of singular points consisting of singular points…