Quantized representation of some nonlinear integrable evolution equations on the soliton sector

The Hirota algorithm for solving several integrable nonlinear evolution equations is suggestive of a simple construction of a quantized representation of these equations and their soliton solutions over a Fock space of bosons or of fermions. The classical nonlinear wave equation becomes a nonlinear equation for an operator. The solution of this equation is constructed through an operator analog of the Hirota transformation. The classical N-soliton solution is the expectation value of the solution operator in an N-particle state in the Fock space. The effect of perturbations that modify soliton identity is demonstrated.