Quantized representation for Kadomtsev-Petviashvili equation on the soliton sector

Details Quantized representation for Kadomtsev-Petviashvili equation on the soliton sector Quantized representation for Kadomtsev-Petviashvili equation on the soliton sector

2011-08-19

arxiv.org/abs/1108.3884v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

Scientific paper

Exploiting the known structure of soliton solutions, obtained through the Hirota transformation, a quantized representation of the Kadomtsev-Petviashvili (KP) equation on the soliton sector is constructed over a Fock space of particles, which may be either bosons or fermions. The classical solution is mapped into an operator, which also obeys the KP equation. The operator is constructed in terms of the particle-number operators. Classical soliton solutions are the expectation values of this operator in multi-particle states in the Fock space. The operator is equation-specific and the state in the Fock space is in one-to-one correspondence with the particular soliton solution.

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