Euler operators and conservation laws of the BBM equation

1979/01/01 by Peter J. Olver · 266 citations
Physics and Astronomy · Mathematics · #Nonlinear Waves and Solitons #Advanced Mathematical Physics Problems #Nonlinear Photonic Systems #Conservation law #Euler equations #Euler's formula #Mathematics #Order (exchange) #Type (biology) #Wave equation #Mathematical analysis #Calculus (dental) #Pure mathematics #Business

paper · doi:10.1017/s0305004100055572

published in Mathematical Proceedings of the Cambridge Philosophical Society 85(1), 143-160 (Cambridge University Press)

openalex publication_date 1979/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

Abstract

Abstract The BBM or Regularized Long Wave Equation is shown to possess only three non-trivial independent conservation laws. In order to prove this result, a new theory of Euler-type operators in the formal calculus of variations will be developed in detail.

Citations

• XLI. On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves
• Solitary-wave interaction
• Korteweg-de Vries Equation and Generalizations. II. Existence of Conservation Laws and Constants of Motion
• Integrals of nonlinear equations of evolution and solitary waves

Cited by

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• Model equations for nonlinear dispersive waves in a compressible Mooney-Rivlin rod
• Tri-Hamiltonian duality between solitons and solitary-wave solutions having compact support
• On the Camassa-Holm equation and a direct method of solution I. Bilinear form and solitary waves
• Benjamin–Bona–Mahony equation [wikipedia]