The quantum theory of solitons and other non-linear classical waves

It has been suspected for some time that certain solutions of non-linear classical field equations indicate that the corresponding quantum theory possesses interesting, even unsuspected properties. A group in Cambridge (U.K. and U.S.A) has developed an approach to the quantum theory which consists of a systematic coupling constant expansion for various quantum mechanical objects: transition amplitudes, S-matrix elements. The first term in this expansion frequently leads to a differential equation which is identical with an equation of the classical theory. Classical equations are encountered in the full quantum theory: they determine lowest order approximations to quantum mechanical objects. Also there is a procedure for calculating higher order corrections. (Auth.)