Global classification of two-component approximately integrable evolution equations

2007/10/11 by Peter H. van der Kamp, van der Kamp, Peter H.
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Fractional Differential Equations Solutions #Nonlinear Waves and Solitons #nlin.SI

paper · pdf · doi:10.48550/arxiv.0710.2233

40 pages, 1 figure, submitted to Foundations of Computational Mathematics, with globally complete description of highest degree divisors, corrected typos and added references

openalex publication_date 2007/10/11 · arxiv created 2008/08/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We globally classify two-component evolution equations, with homogeneous diagonal linear part, admitting infinitely many approximate symmetries. Important ingredients are the symbolic calculus of Gel'fand and Dikii, the Skolem-Mahler-Lech theorem, results on diophantine equations in roots of unity by F. Beukers, and an algorithm of C.J. Smyth.

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