000014022 001__ 14022
000014022 005__ 20161115094008.0
000014022 04107 $$aeng
000014022 046__ $$k2016-08-21
000014022 100__ $$aRzeznik, Andrew
000014022 24500 $$aEnergy propagation and group speed for complex exponential waves

000014022 24630 $$n24.$$p24th International Congress of Theoretical and Applied Mechanics - Book of Papers
000014022 260__ $$bInternational Union of Theoretical and Applied Mechanics, 2016
000014022 506__ $$arestricted
000014022 520__ $$2eng$$aIn classical dispersive wave equations, the solution is specified by a superposition of plane waves of the form exp(i(k · x − ωt)) (with k and ω real valued) along with a dispersion relation G(ω, k) = 0. However, in many problems one needs to consider solutions of the form exp(d · x + st), where d and s are complex and correspondingly related by G(is, −id) = 0. In these cases the classical theory providing the speed and direction of the energy propagation no longer applies. In this paper we derive general energy propagation formulas for generic complex exponential wave solutions. We show that: parallel to the direction of the exponential spatial envelope, the energy propagation speed is ce∥ = −Re(s)/Re(d∥ ), while in the orthogonal directions it is cei⊥ = −∂Im(s)/∂Im(di⊥ ). In the classical limit this is consistent with the standard group velocity.

000014022 540__ $$aText je chráněný podle autorského zákona č. 121/2000 Sb.
000014022 653__ $$a

000014022 7112_ $$a24th International Congress of Theoretical and Applied Mechanics$$cMontreal (CA)$$d2016-08-21 / 2016-08-26$$gICTAM2016
000014022 720__ $$aRzeznik, Andrew
000014022 8560_ $$ffischerc@itam.cas.cz
000014022 8564_ $$s74202$$uhttps://invenio.itam.cas.cz/record/14022/files/PO.FM16-1.04.187.pdf$$yOriginal version of the author's contribution as presented on CD, XMLout( page 1636, code PO.FM16-1.04.187).
000014022 962__ $$r13812
000014022 980__ $$aPAPER