The statistical performance analysis of ESPRIT, root-MUSIC, minimum-norm methods for direction estimation, due to "nite data perturbations, using the modi"ed spatially smoothed covariance matrix, is developed. Expressions for the mean-squared error in the direction estimates are derived based on a common framework. Based on the analysis, the use of the modi"ed smoothed covariance matrix improve...

We prove that the KdV-Burgers is globally well-posed in H−1(T) with a solution-map that is analytic fromH−1(T) to C([0, T ];H−1(T)) whereas it is ill-posed in Hs(T), as soon as s < −1, in the sense that the flow-map u0 7→ u(t) cannot be continuous from H s(T) to even D′(T) at any fixed t > 0 small enough. In view of the result of Kappeler and Topalov for KdV it thus appears that even if the dis...

A wide variety of different physical systems can be described by a relatively small set of universal equations. For example, small-amplitude nonlinear Schrödinger dark solitons can be described by a Korteweg-de Vries (KdV) equation. Reductive perturbation theory, based on linear boosts and Gallilean transformations, is often employed to establish connections to and between such universal equati...

In this paper we study weak continuity of the dynamical systems for the KdV equation in H−3/4(R) and the modified KdV equation in H1/4(R). This topic should have significant applications in the study of other properties of these equations such as finite time blow-up and asymptotic stability and instability of solitary waves. The spaces considered here are borderline Sobolev spaces for the corre...

The KdV equation is the canonical example of an integrable nonlinear partial differential equation supporting multi-soliton solutions. Seeking to understand the nature of this interaction, we investigate different ways to write the KdV 2-soliton solution as a sum of two or more functions. The paper reviews previous work of this nature and introduces new decompositions with unique features, putt...

in this paper we investigate a nonlinear evolution model described by the rosenau-kdv equation. we propose a three-level average implicit finite difference scheme for its numerical solutions and prove that this scheme is stable and convergent in the order of o(τ2 + h2). furthermore we show the existence and uniqueness of numerical solutions. comparing the numerical results with other methods in...

In this paper, we establish exact solutions for the timefractional Klein-Gordon equation, and the time-fractional HirotaSatsuma coupled KdV system. The Hes semi-inverse and the Kudryashov methods are used to construct exact solutions of these equations. We apply Hes semi-inverse method to establish a variational theory for the time-fractional Klein-Gordon equation, and the timefractional Hirota...

We show how the supersymmetric KdV equation can be obtained from the self–duality condition on Yang–Mills fields in four dimension associated with the graded Lie algebra OSp(2/1). We also obtain the hierarchy of Susy KdV equations from such a condition. We formulate the Susy KdV hierarchy as a vanishing curvature condition associated with the U(1) group and show how an Abelian self–duality cond...

Designs are often modi ed for use in new circumstances. If formal proof is to be an acceptable veri cation methodology for industry, it must be capable of tracking design changes quickly. We describe our experiences formally verifying an implementation of an ATM network component, and on our subsequent veri cation of modi ed designs. Three of the designs veri ed are in use in a working network....

In a previous paper we proved that long-wavelength solutions of the waterwave problem in the case of zero surface tension split up into two wave packets, one moving to the right and one to the left, where each of these wave packets evolves independently as a solution of a Korteweg-de Vries (KdV) equation. In this paper we examine the effect of surface tension on this scenario. We find that we o...