Quantum and Classical Statistical Mechanics of the Non-Linear Schrödinger, Sinh-Gordon and Sine-Gordon Equations

  • R. K. Bullough
  • D. J. Pilling
  • J. T. Timonen
Conference paper
Part of the Springer Series in Synergetics book series (SSSYN, volume 30)

Abstract

We are going to describe our work on the quantum and classical statistical mechanics of some exactly integrable non-linear one dimensional systems. The simplest is the non-linear Schrödinger equation (NLS)
$$i{\psi _t} = - {\psi _{XX}} + 2c{\psi ^ + }\psi \psi $$
(1)
where c, the coupling constant, is positive. The others are the sine- and sinh-Gordon equations (sG and shG)
$${\phi _{xx}} - {\phi _{tt}} = {m^2}\sin \phi $$
(1.2)
$${\phi _{xx}} - {\phi _{tt}} = {m^2}\sinh \phi $$
(1.3)

Keywords

Soliton Peri Sine 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1985

Authors and Affiliations

  • R. K. Bullough
    • 1
  • D. J. Pilling
    • 1
  • J. T. Timonen
    • 2
  1. 1.Department of MathematicsUMISTManchesterGreat Britain
  2. 2.Department of PhysicsUniversity of JyväskyläJyväskyläFinland

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