In this paper we deal with the almost classical problem of the energy propagation associated with a given dispersive wave motion. Usually, in the literature the energy-flux velocity is assumed to specify this propagation, and it is known simply as energy velocity. For homogeneous monochromatic waves propagating in a linear isotropic system with dispersion but without dissipation, this velocity ...

In this paper, we construct some interesting Gevrey functions of order α for every α > 1 with compact support by a clever use of the Bray-Mandelbrojt iterative process. We then apply these results to the moment method, which will enable us to derive some upper bounds for the cost of fast boundary controls for a class of linear equations of parabolic or dispersive type that partially improve the...

Abstract. There exist several approaches for the parallel solving of huge systems of linear equations resulting from the finite element (f.e.) discretization of 2nd order elliptic pdes. On the other hand, there exists a great demand for Algebraic Multigrid solvers (AMG) which have as input only matrix and right hand side or, as a substitute, the appropriate information per element. In this pape...

We introduce a nonlinear dispersive quintic equation. Its travelling waves are governed by a linear equation. We construct a large variety of explicit compact solitary waves. Some of these compactons are very robust, others decompose very quickly. Numerical simulations also reveal the existence of compact travelling breathers. c © 1999 Published by Elsevier Science B.V.

A tool for the order reduction of differential algebraic equations (DAEs) is outlined in this report. Through the use of an equation dependency analysis and nonlinear function approximation, the algebraic equations can be divided into sets that require implicit or explicit solutions. If all of the algebraic variables can be solved or approximated explicitly, the DAE becomes a set of ordinary di...

This paper presents two models typical of two different approaches often used for modelling the advective-dispersive transport of multiple ions in variably-saturated porous media. The first approach assumes that all solute reactions can be incorporated directly into the governing transport equations (the one-step method), while the second approach divides the mathematical solution process into ...

A Dispersive Wave Equation in 2 + 1 dimensions (2LDW) widely discussed by different authors is shown to be nothing but the modified version of the Generalized Dispersive Wave Equation (GLDW). Using Singularity Analysis and techniques based upon the Painlevé Property leading to the Double Singular Manifold Expansion we shall find the Miura Transformation which converts the 2LDW Equation into the...

Abstract The reduced modified Ostrovsky equation is a reduction of the modified Korteweg-de Vries equation, in which the usual linear dispersive term with a third-order derivative is replaced by a linear non-local integral term, representing the effect of background rotation. Here we study the case when the cubic nonlinear term has the same polarity as the rotation term. This equation is integr...

The aim of this article is to describe asymptotic profiles for the Kirchhoff equation, and to establish time decay properties and dispersive estimates for Kirchhoff equations. For this purpose, the method of asymptotic integration is developed for the corresponding linear equations and representation formulae for their solutions are obtained. These formulae are analysed further to obtain the ti...

We discuss the solution of linear second order differential-algebraic equations (DAEs) with variable coefficients. Since index reduction and order reduction for higher order, higher index differential-algebraic systems do not commute, appropriate index reduction methods for higher order DAEs are required. We present an index reduction method based on derivative arrays that allows to determine a...