Energy Propagation in Dissipative Systems. Part 2: Centrovelocity for NonlinearWave Equations

摘要

Nonlinear wave equations, first order in time, of a specific form, areconsidered. In the absence of dissipation, these equations are given by a Poisson system, with the Hamiltonian that is the integral of some density. The functional I, defined to be the integral of the square of the waveform, is a constant of motion of the unperturbed system. Z, the center of gravity of this density, is shown to be canonically conjugate to I and can be used as a measure to locate the position of the waveform. By introducing new coordinates based on Z, expressions for the centrovelocity of Z and the decay of I, which compare to the lines of the previous first part of this study, in both the conservative and the dissipative case, are obtained. With the derived expressions, the decay of solitary waves of the Korterweg de Vries equation, when different kinds of dissipation are added, is investigated.