Related papers: Whitham systems and deformations
This is essentially a survey paper in which we solve the global Cauchy problem on causal manifolds for hyperbolic systems of linear partial differential equations in the framework of hyperfunctions. Besides the classical Cauchy-Kowalevsky…
Decomposition systems with rapidly decaying elements (needlets) based on Hermite functions are introduced and explored. It is proved that the Triebel-Lizorkin and Besov spaces on $\R^d$ induced by Hermite expansions can be characterized in…
Based on the well-established theory of discrete conjugate nets in discrete differential geometry, we propose and examine discrete analogues of important objects and notions in the theory of semi-Hamiltonian systems of hydrodynamic type. In…
We study the null space degeneracy of open quantum systems with multiple non-Abelian, strong symmetries. By decomposing the Hilbert space representation of these symmetries into an irreducible representation involving the direct sum of…
The aim of this paper is to show how a weakly dispersive perturbation of the inviscid Burgers equation improve (enlarge) the space of resolution of the local Cauchy problem. More generally we will review several problems arising from weak…
A great number of works is devoted to qualitative investigation of Hamiltonian systems. One of tools of such investigation is the method of skew-symmetric differential forms. In present work, under investigation Hamiltonian systems in…
We define branched bending deformations as deformations supported on a piecewise totally geodesic complex of $(n-1)$-dimensional faces meeting along $(n-2)$-dimensional branching loci. These are a generalization of bending deformations, as…
This paper gives an exposition of the authors' harmonic deformation theory for 3-dimensional hyperbolic cone-manifolds. We discuss topological applications to hyperbolic Dehn surgery as well as recent applications to Kleinian group theory.…
We give sufficient conditions for the uniform hyperbolicity of certain nonuniformly hyperbolic dynamical systems. In particular, we show that local diffeomorphisms that are nonuniformly expanding on sets of total probability are necessarily…
The main purpose of this article is to develop an explicit derived deformation theory of algebraic structures at a high level of generality, encompassing in a common framework various kinds of algebras (associative, commutative, Poisson...)…
Whitham theory of modulations is developed for periodic waves described by nonlinear wave equations integrable by the inverse scattering transform method associated with $2\times2$ matrix or second order scalar spectral problems. The theory…
We report experimental observations of an undulational instability of myelin figures. Motivated by this, we examine theoretically the deformation and possible instability of concentric, cylindrical, multi-lamellar membrane structures. Under…
The classical global linearization theorem for autonomous system given in [C. Pugh, Amer. J. Math., 91 (1969) 363-367] requires that nonlinear system with hyperbolicity satisfies boundedness and Lipschitz continuity.In this paper, we…
We revisit the nonlinear second-order differential equations $$ \ddot{x}(t)=a (x )\dot{x}(t)^2+b(t)\dot{x}(t) $$ where $a(x)$ and $b(t)$ are arbitrary functions on their argument from the perspective of Lie-Hamilton systems. For the…
We propose a simple construction of the non-Hamiltonian dynamical systems possessing an invariant measure. These non-Hamiltonian systems are deformations of the Hamiltonian systems associated with trivial deformations of the canonical…
Main mathematical applications of Frobenius manifolds are in the theory of Gromov - Witten invariants, in singularity theory, in differential geometry of the orbit spaces of reflection groups and of their extensions, in the hamiltonian…
In the first part of this paper, we give a new analytical proof of a theorem of C. Sabbah on integrable deformations of meromorphic connections on $\mathbb P^1$ with coalescing irregular singularities of Poincar\'e rank 1, and generalizing…
We consider the Hurwitz spaces of ramified coverings of $\mathbb{P}^1$ with prescribed ramification profile over the point at infinity. By means of a particular symmetric bidifferential on a compact Riemann surface, we introduce…
B. Dubrovin introduced the structure of a Dubrovin--Frobenius manifold on a space of ramified coverings of a sphere by a genus $g$ Riemann surface with the prescribed ramification profile. This is now known as a genus $g$ Hurwitz--Frobenius…
We develop a theory for distributed branch points and investigate their role in determining the shape and influencing the mechanics of thin hyperbolic objects. We show that branch points are the natural topological defects in hyperbolic…