Open Access. Powered by Scholars. Published by Universities.®

Partial Differential Equations Commons™

Open Access. Powered by Scholars. Published by Universities.®

Dynamic Systems

Institution
Keyword
Publication Year
Publication
Publication Type
File Type

Articles 61 - 68 of 68

Full-Text Articles in Partial Differential Equations

Water Waves And Integrability, Rossen Ivanov Jan 2007

Water Waves And Integrability, Rossen Ivanov

Articles

The Euler’s equations describe the motion of inviscid fluid. In the case of shallow water, when a perturbative asymtotic expansion of the Euler’s equations is taken (to a certain order of smallness of the scale parameters), relations to certain integrable equations emerge. Some recent results concerning the use of integrable equation in modeling the motion of shallow water waves are reviewed in this contribution.

Go to article

Generalised Fourier Transform For The Camassa-Holm Hierarchy, Adrian Constantin, Vladimir Gerdjikov, Rossen Ivanov Jan 2007

Generalised Fourier Transform For The Camassa-Holm Hierarchy, Adrian Constantin, Vladimir Gerdjikov, Rossen Ivanov

Articles

The squared eigenfunctions of the spectral problem associated to the Camassa-Holm equation represent a complete basis of functions, which helps to describe the Inverse Scattering Transform for the Camassa-Holm hierarchy as a Generalised Fourier transform. The main result of this work is the derivation of the completeness relation for the squared solutions of the Camassa-Holm spectral problem. We show that all the fundamental properties of the Camassa-Holm equation such as the integrals of motion, the description of the equations of the whole hierarchy and their Hamiltonian structures can be naturally expressed making use of the completeness relation and the recursion …

Go to article

Inverse Scattering Transform For The Camassa-Holm Equation, Adrian Constantin, Vladimir Gerdjikov, Rossen Ivanov Jan 2006

Inverse Scattering Transform For The Camassa-Holm Equation, Adrian Constantin, Vladimir Gerdjikov, Rossen Ivanov

Articles

An Inverse Scattering Method is developed for the Camassa-Holm equation. As an illustration of our approach the solutions corresponding to the reflectionless potentials are constructed in terms of the scattering data. The main difference with respect to the standard Inverse Scattering Transform lies in the fact that we have a weighted spectral problem. We therefore have to develop different asymptotic expansions.

Go to article

Multivalued Logic, Neutrosophy And Schrodinger Equation, Florentin Smarandache, Victor Christianto Dec 2005

Multivalued Logic, Neutrosophy And Schrodinger Equation, Florentin Smarandache, Victor Christianto

Branch Mathematics and Statistics Faculty and Staff Publications

This book was intended to discuss some paradoxes in Quantum Mechanics from the viewpoint of Multi-Valued-logic pioneered by Lukasiewicz, and a recent concept Neutrosophic Logic. Essentially, this new concept offers new insights on the idea of ‘identity’, which too often it has been accepted as given. Neutrosophy itself was developed in attempt to generalize Fuzzy-Logic introduced by L. Zadeh. While some aspects of theoretical foundations of logic are discussed, this book is not intended solely for pure mathematicians, but instead for physicists in the hope that some of ideas presented herein will be found useful. The book is motivated by …

Go to article

Conformal Properties And Baecklund Transform For The Associated Camassa-Holm Equation, Rossen Ivanov Jan 2005

Conformal Properties And Baecklund Transform For The Associated Camassa-Holm Equation, Rossen Ivanov

Articles

Integrable equations exhibit interesting conformal properties and can be written in terms of the so-called conformal invariants. The most basic and important example is the KdV equation and the corresponding Schwarz-KdV equation. Other examples, including the Camassa-Holm equation and the associated Camassa-Holm equation are investigated in this paper. It is shown that the B¨acklund transform is related to the conformal properties of these equations. Some particular solutions of the Associated Camassa-Holm Equation are discussed also.

Go to article

Solitary Waves In Layered Nonlinear Media, Randall J. Leveque, Darryl H. Yong Jun 2003

Solitary Waves In Layered Nonlinear Media, Randall J. Leveque, Darryl H. Yong

All HMC Faculty Publications and Research

We study longitudinal elastic strain waves in a one-dimensional periodically layered medium, alternating between two materials with different densities and stress-strain relations. If the impedances are different, dispersive effects are seen due to reflection at the interfaces. When the stress-strain relations are nonlinear, the combination of dispersion and nonlinearity leads to the appearance of solitary waves that interact like solitons. We study the scaling properties of these solitary waves and derive a homogenized system of equations that includes dispersive terms. We show that pseudospectral solutions to these equations agree well with direct solutions of the hyperbolic conservation laws in the …

Go to article

Dynamics And Control Of A Three Dimensional Gantry Crane With Cable Flexibility, Uchendu H. Eke Oct 1996

Dynamics And Control Of A Three Dimensional Gantry Crane With Cable Flexibility, Uchendu H. Eke

Mechanical & Aerospace Engineering Theses & Dissertations

The control of payload swing in industrial gantry cranes is a topic of widespread interest. In this thesis, the control of the swing of a payload idealized by a point mass assumption is investigated utilizing s, compact robotics matrix/vector representation of the dynamical model. In this form, this particular system can be viewed as sn underactuated manipulator with equal numbers of active and passive degrees of freedom. The full three dimensional model is developed and linearized by modelling the cable as a single thread of fiexible wire and the degree of dynamic coupling between the active and passive coordinates is …

Go to article

A Mathematical Model And Simulation Of Natural Circulation Loop Thermalhydraulics, Nihad E. Daidzic Mar 1992

A Mathematical Model And Simulation Of Natural Circulation Loop Thermalhydraulics, Nihad E. Daidzic

Aviation Department Publications

In this work, a simple, nonlinear, seventh-order mathematical model with lumped parameter analysis of the thermalhydraulic processes in a natural circulation steam boiler loop is presented. Digital simulation has been performed in order to predict open loop transients in severe accidental situations. Parts of the circulation loop such as the steam drum, downcomer, and riser were modelled separately on the basis of the integral balance equations. The two-phase flow in the steam drum and in the riser was modelled with the aid of a homogeneous-equilibrium, two-phase flow model. Special care was taken to ensure the stability of the numerical scheme, …

Go to article

First Prev