On the Linear Equations of Soliton Theory
During the past few years there has been an increasing interest in solitons. The soliton and its remarkable properties are well known to those already familiar with the history of coherent optics since one of the earliest examples of a soliton was the 2π pulse of self-induced transparency . In that instance a satisfactory mathematical setting for the soliton was completely provided by the coupled Maxwell and Schroedinger-Bloch equations. The situation is not as satisfactory in regard to the equations that have more recently been shown to exhibit soliton behavior, however. To solve these equations, certain linear equations analogous to the equations for the two-level atom have been introduced  in a somewhat ad hoc fashion.
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