Functional Equations and Poincare Invariant Mechanical Systems

2001/10/09 by J. G. B. Byatt-Smith, J. G. B. Byatt‐Smith, Byatt-Smith, J. G. B. +2
Mathematics · Physics and Astronomy · #30D05 #33E05 #39B32 #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Numerical methods for differential equations #Quantum chaos and dynamical systems #math-ph #math.MP #msc:30D05 #msc:33E05 #msc:39B32

paper · pdf · doi:10.48550/arxiv.math-ph/0110012

22 pages LaTeX

arxiv created 2001/10/09 · openalex publication_date 2001/10/09 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the following functional equation that has arisen in the context of mechanical systems invariant under the Poincare algebra: ∑_i=1ⁿ⁺¹\dfrac∂∂ x_i∏_{j≠ i}f(x_i-x_j) =0, n ≥ 2. New techniques are developed and the general solution within a certain class of functions is given. New solutions are found.

Citations

• Integrable Systems with Pairwise Interactions and Functional Equations

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