Retarded reflection of dispersive wave packets in a star-shaped network.

Retarded reflection of dispersive wave packets in a star-shaped network. We study Klein-Gordon equations on two half-axes with different dispersion relations. The reflection coefficient at the connecting point depends on the frequency. We obtain lower and upper bounds of the reflected part of the energy flow when the frequency band involved in the initial signal is sufficiently narrow. The reflection is delayed for low frequency wave packets and our expression of the delay is in accordance with the recent experiments of Haibel and Nimtz (Ann. Physik (Leipzig) 10 (2001) 707-712). The results are generalized to the case of a star-shaped network with n branches (n > 2). (C) 2003 Academie des sciences. Publie par Editions scientifiques et medicales Elsevier SAS. Tous droits reserves.