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

TL;DR

This paper proposes a quantum-inspired framework for representing integrable nonlinear evolution equations and their soliton solutions using operator methods and Fock space, bridging classical soliton theory with quantum operator formalism.

Contribution

It introduces a novel quantized operator representation of integrable equations and soliton solutions, extending classical methods into a quantum operator context.

Findings

Operator form of nonlinear equations derived

Soliton solutions expressed as expectation values in Fock space

Classical N-solitons obtained from quantum operator solutions

Abstract

The Hirota algorithm for solving several integrable nonlinear evolution equations is suggestive of a simple 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 the operator analog of the Hirota transformation. The classical N-solitons solution is the expectation value of the solution operator in an N-particle state in the Fock space.