The soliton number of optical soliton bound states for two special families of input pulses

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Abstract
To gain a better understanding of the generation of optical solitons the author investigates the linear eigenvalue problem associated with the non-linear Schrodinger equation. Two families of initial envelope functions are discussed. It is found that, for a purely imaginary initial envelope function of width a and height b, and its Galilei transforms, the soliton number of soliton bound states is the integer smaller than 1/2+ab/ pi . For the initial envelope function i beta exp(- alpha mod x mod ) and its Galilei transforms, the soliton number of soliton bound states is equal to the number of intersections of the Bessel functions J-1/2 and +or-J1/2 below beta / alpha , which is the integer smaller than 1/2+2 beta / alpha pi .