A method for obtaining analytical expressions for $2N\pi$ pulses in an unbroadened resonant medium is derived by a systematic application of the Bäcklund transformation. The resulting large-area pulses display the expected property of pulse breakup into separate $2\pi$ hyperbolic secant pulses.

• Received 11 September 1972

DOI:https://doi.org/10.1103/PhysRevA.7.373