相关论文: The Camassa--Holm Equation and The String Density …

In this paper we consider a class of isospectral deformations of the inhomogeneous string boundary value problem. The deformations considered are generalizations of the isospectral deformation that has arisen in connection with the…

The inverse problem which arises in the Camassa--Holm equation is revisited for the class of discrete densities. The method of solution relies on the use of orthogonal polynomials. The explicit formulas are obtained directly from the…

Motivated by the study of certain nonlinear wave equations (in particular, the Camassa-Holm equation), we introduce a new class of generalized indefinite strings associated with differential equations of the form…

We consider a dynamic inverse problem for a dynamical system which describes the propagation of waves in a Krein string. The problem is reduced to an integral equation and an important special case is considered when the string density is…

An extension of the Camassa-Holm hierarchy is constructed in this letter. The conserved quantities of the hierarchy are studied and a recurrent formula for the integrals of motion is derived.

We review some recent developments in the theory of $W_\infty$. We comment on its relevance to lower-dimensional string theory.

Recent developments in cosmic strings are reviewed, with emphasis on unresolved problems.

We study the propagation of energy density in finite-energy weak solutions of the Camassa-Holm and related equations. Developing the methods based on generalized nonunique characteristics, we show that the parts of energy related to…

We review some recent developments in string theory, emphasizing the importance of vacuum instabilities, their relation to the density of states, and the role of space-time fermions in non-critical string theory. We also discuss the…

We review recent developments in the field of string cosmology with particular emphasis on open problems having to do mainly with geometric asymptotics and singularities. We discuss outstanding issues in a variety of currently popular…

We obtain systematic approximations for the modes of vibration of a string of variable density, which is held fixed at its ends. These approximations are obtained iteratively applying three theorems which are proved in the paper and which…

Cosmic strings, topological defects predicted by high-energy theories, may contribute to the late-time expansion of the Universe, effectively mimicking dynamical dark energy. We investigate four phenomenological extensions of the…

We analyze the problem of calculating the solutions and the spectrum of a string with arbitrary density and fixed ends. We build a perturbative scheme which uses a basis of WKB-type functions and obtain explicit expressions for the…

We discuss the generation and evolution of density perturbations during the large curvature phase of string cosmology. We find that perturbations in the scalar components of the metric evolve with cosmic time as $\exp (\gamma H_st)$ where…

In this paper we construct a global, continuous flow of solutions to the Camassa-Holm equation on the space H^1(R). In a previous paper [2], A. Bressan and the author constructed spatially periodic solutions, whereas in this paper the…

The time evolution of an oscillator coupled to an infinite string with a discontinuous mass density is investigated. It is shown that the equation of motion of the oscillator leads to a nonlinear characteristic equation due to the…

We extend the Euler-Bernoulli beam problem, formulated as a matrix string equation with a matrix-valued density, to a setting where the density takes values in a Clifford algebra, and we analyze its isospectral deformations. For discrete…

A new approach to the Euler-Bernoulli beam based on an inhomogeneous matrix string problem is presented. Three ramifications of the approach are developed: (1) motivated by an analogy with the Camassa-Holm equation a class of isospectral…

We present concrete solutions with accelerated expansion in string theory, requiring a small, tractable list of stress energy sources. We explain how this construction (and others in progress) evades previous no go theorems for simple…

We establish an exponential stabilization result for linear port-Hamiltonian systems of first order with quite general, not necessarily continuous, energy densities. In fact, we have only to require the energy density of the system to be of…