A weighted least action principle for dispersive waves
نویسنده
چکیده
We extend the least action principle to continuum systems. The data for the new principle consists of the intensity of the wave (or rather the wave action) at two instances of time. We define an appropriate Lagrangian, and formulate a variational problem in terms of it. The critical points of the functional are used to determine the wave’s phase. The theory is applicable to the semiclassical limit of a large class of dispersive wave equations. Associating the wave equation with a Liouville equation for the Wigner distribution function, we are able to extend the theory to include singular solutions such as caustics.
منابع مشابه
Introduction to Quantum Mechanics
Printed and bound in Great Britain by Antony Rowe Ltd, Chippenham, Wiltshire This book is printed on acid-free paper responsibly manufactured from sustainable forestry, in which at least two trees are planted for each one used for paper production. Contents Foreword xi Editor's preface to the Manchester Physics Series xiii Author's preface xv 1 PLANCK'S CONSTANT IN ACTION 1.1 Photons 1 1.2 De B...
متن کاملA new form of governing equations of fluids arising from Hamilton's principle
A new form of governing equations is derived from Hamilton’s principle of least action for a constrained Lagrangian, depending on conserved quantities and their derivatives with respect to the time-space. This form yields conservation laws both for non-dispersive case (Lagrangian depends only on conserved quantities) and dispersive case (Lagrangian depends also on their derivatives). For non-di...
متن کاملLarge Scale Experiments Data Analysis for Estimation of Hydrodynamic Force Coefficients Part 1: Time Domain Analysis
This paper describes various time-domain methods useful for analyzing the experimental data obtained from a circular cylinder force in terms of both wave and current for estimation of the drag and inertia coefficients applicable to the Morison’s equation. An additional approach, weighted least squares method is also introduced. A set of data obtained from experiments on heavily roughened circul...
متن کاملAnalysis and Design of Dispersive Interdigital Surface-Wave Transducers
A comprehensive circuit model characterization of dispersive interdigital transducers with nonuniform electrode spacing is presented. The model is an extension of a three-port circuit which has been useful for representing periodic transducers. The extended model includes the effects of strong piezoelectric coupling whereby the acoustic waves and electric circuits interact, and it also accounts...
متن کاملBifurcation diagram of a one-parameter family of one-dimensional nonlinear dispersive waves
The KdV equation with small dispersion is a model for the formation and propagation of dispersive shock waves. Dispersive shock waves are characterized by the appearance of modulated oscillations nearby the breaking point. The modulation in time and space of the amplitude, the frequencies and the wave-numbers of these oscillations is described by the g-phase Whitham equations. We study the init...
متن کامل