On a quaternionic form of the Maxwell equations for the time-dependent electromagnetic field in chiral media

In [1] a quaternionic reformulation of the time-harmonic Maxwell equations for chiral media was proposed and used in [2] in order to construct complete systems of quaternionic fundamental solutions convenient for numerical analysis of scattering boundary value problems. In the present contribution we give a quaternionic reformulation of time-dependent Maxwell's equations for chiral media. The Maxwell system is written as a single quaternionic equation. We obtain a fundamental solution of this equation and use it for solving Maxwell's system with sources. This is a joint work with V. V. Kravchenko. [1] Khmelnytskaya, K. V., Kravchenko, V. V. and H. Oviedo: Quaternionic integral representations for electromagnetic fields in chiral media. Telecommunications and Radio Engineering 56 (2001), # 4&5, 53-61. [2]Khmelnytskaya, K. V. , Kravchenko, V. V. and V. S. Rabinovich: Quaternionic Fundamental Solutions for Electromagnetic Scattering Problems and Application. Zeitschrift für Analysis und ihre Anwendungen 22 (2003), 147--166.