Lagrangians and integrability for additive fourth-order difference equations

2019/10/24 by Giorgio Gubbiotti, Gubbiotti, Giorgio
Mathematics · Medicine · Physics and Astronomy · #37K10 #39A10 #70S05 #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph) #Mathematical and Theoretical Epidemiology and Ecology Models #Nonlinear Differential Equations Analysis #Nonlinear Waves and Solitons #math-ph #math.MP #msc:37K10 #msc:39A10 #msc:70S05 #nlin.SI

paper · pdf · doi:10.48550/arxiv.1910.11458

40 pages, 1 figure

arxiv created 2019/10/24 · openalex publication_date 2019/10/24 · arxiv updated 2019/10/28 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28

Abstract

We use a recently found method to characterise all the invertible fourth-order difference equations linear in the extremal values based on the existence of a discrete Lagrangian. We also give some result on the integrability properties of the obtained family and we put it in relation with known classifications. Finally, we discuss the continuum limits of the integrable cases.

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