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Classical and quantum operator nonlinear schrodinger equation. I

2. Completely Integrable Systems

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Part of the Lecture Notes in Mathematics book series (LNM,volume 925)

Abstract

We consider generalizations of the classical nonlinear Schrödinger equation, iψt = ψxx + 2ψψ+ψ, to operator functions ψ=ψ(x,t) and their solvability via the inverse scattering method. This provides a new class of soluble field theories in one-space, one-time dimensions, which, after quantization, are equivalent to a system of many, nonidentical, particles with σ-function interactions and a spectrum of bound states richer than in the usual model.

Keywords

  • Spectral Problem
  • Schrodinger Equation
  • Nonlinear Schrodinger Equation
  • Inverse Scattering Method
  • Hamiltonian Flow

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© 1982 Springer-Verlag

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Chudnovsky, D.V., Chudnovsky, G.V., Neveu, A. (1982). Classical and quantum operator nonlinear schrodinger equation. I. In: Chudnovsky, D.V., Chudnovsky, G.V. (eds) The Riemann Problem, Complete Integrability and Arithmetic Applications. Lecture Notes in Mathematics, vol 925. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0093507

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  • DOI: https://doi.org/10.1007/BFb0093507

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11483-3

  • Online ISBN: 978-3-540-39152-4

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