Comments on Nonlinear Wave Equations as Models for Elementary Particles
1964/09/01 by G. H. Derrick · 1,419 citations
Mathematics · Physics and Astronomy · #Class (philosophy) #Classical mechanics #Computer science #Energy (signal processing) #Mathematical analysis #Mathematics #Nonlinear Photonic Systems #Nonlinear system #Physics #Quantum Mechanics and Applications #Quantum chaos and dynamical systems #Quantum mechanics #Wave equation #Wave function
paper · pdf · doi:10.1063/1.1704233
published in Journal of Mathematical Physics 5(9), 1252-1254 (American Institute of Physics)
openalex publication_date 1964/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
Abstract
It is shown that for a wide class of nonlinear wave equations there exist no stable time-independent solutions of finite energy. The possibility is considered whether elementary particles might be oscillating solutions of some nonlinear wave equation, in which the wavefunction is periodic in the time though the energy remains localized.
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