Quantized representation of some nonlinear integrable evolution equations on the soliton sector
Exactly Solvable and Integrable Systems
2015-05-19 v1 Mathematical Physics
math.MP
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.
Keywords
Cite
@article{arxiv.1007.3221,
title = {Quantized representation of some nonlinear integrable evolution equations on the soliton sector},
author = {Yair Zarmi},
journal= {arXiv preprint arXiv:1007.3221},
year = {2015}
}
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12 pages