Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2010-07-19
Physical Review E 83, 056606 (2011)
Nonlinear Sciences
Exactly Solvable and Integrable Systems
12 pages
Scientific paper
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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