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

2010/07/19 by Yair Zarmi · 5 citations
Mathematics · Physics and Astronomy · #Boson #Fock space #Fock state #Integrable system #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Nonlinear system #Operator (biology) #Physics #Quantum Mechanics and Non-Hermitian Physics #Quantum mechanics #Representation (politics) #Soliton #Space (punctuation) #math-ph #math.MP #nlin.SI

paper · pdf · doi:10.1103/physreve.83.056606

published in Physical Review E 83(5), 056606 (American Physical Society) · 12 pages

arxiv created 2010/07/19 · openalex publication_date 2011/05/13 · arxiv updated 2015/05/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

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.

Citations

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