The Painleve test, Backlund transformation and solutions of the reduced Maxwell-Bloch equations

The Painleve property for partial differential equations (PDES) proposed by Weiss et al. (1983) is studied for a system of PDES, namely the reduced Maxwell-Bloch (RMB) equations. The RMB equations describe the propagation of short optical pulses through dielectric materials with a resonant non-degenerate transition. The author demonstrates that the RMB system passes the Painleve test, and constructs a Backlund transformation and solutions of the RMB equations.

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