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Splitting of energy of dispersive waves in a star‐shaped network
Author(s) -
Mehmeti F. Ali,
Régnier V.
Publication year - 2003
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.200310010
Subject(s) - star (game theory) , energy (signal processing) , dispersion (optics) , klein–gordon equation , laplace transform , wave equation , physics , state (computer science) , type (biology) , node (physics) , mathematics , mathematical physics , mathematical analysis , quantum mechanics , geology , algorithm , paleontology , nonlinear system
We study wave and Klein‐Gordon equations in a star‐shaped network. In the wave case we state a d'Alembert‐type solution formula generalizing the formula obtained in Ali Mehmeti [1] and [4] for four branches. In the Klein‐Gordon case (dispersive waves) we solve the problem using the Laplace transform with respect to time. We state a continuity equation linking the energy density and the energy flow for the Klein‐Gordon equation in a star‐shaped network. We observe that the splitting of energy at the central node is the same for propagating waves with and without dispersion.