EIGENVALUES OF THE ZAKHAROV-SHABAT EQUATIONS BY SEMICLASSICAL APPROXIMATION

The Zakharov-Shabat equations are solved using the semiclassical phase-integral formalism. The results are discussed in relation to the creation of soliton pulses of a phase-modulated optical pulse in an optical fibre or two-level medium. Following the method of Crothers and Stueckelberg, the quantisation of a complex phase-integral of an adiabatic action is proposed as a criterion for the existence of such solutions. The formula is found to accord with the class of exact solutions of Kunicke's model. A formula is also proposed for a simple phase-modulated step pulse.