Sine-Gordon Equation

1970/01/01 by Julio Rubinstein · 345 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Classical mechanics #Computer science #Connection (principal bundle) #Covariance #Exact differential equation #Field (mathematics) #First-order partial differential equation #Geometry #Hill differential equation #Korteweg–de Vries equation #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Nonlinear system #Partial differential equation #Physics #Pure mathematics #Quantum mechanics #Soliton #Stability (learning theory) #sine-Gordon equation

paper · doi:10.1063/1.1665057

published in Journal of Mathematical Physics 11(1), 258-266 (American Institute of Physics)

openalex publication_date 1970/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

The equation φtt − φxx + m2 sin φ = 0 is presented as a model field theory and studied in detail. It exhibits discrete conserved quantities and extended particle states, with the proper behavior regarding covariance, stability, etc. Those particles do not interact with small oscillations, and we show that this (plus a few reasonable requirements) defines the model uniquely. A connection with the Korteweg-de Vries equation, which has similar properties, is established.

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