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arXiv · 1007.3221

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

Yair Zarmi
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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.

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Yair Zarmi. 2010-07-19. Quantized representation of some nonlinear integrable evolution equations on the soliton sector. https://doi.org/10.1103/physreve.83.056606

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