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.

Lagrangians and integrability for additive fourth-order difference equations / G. Gubbiotti. - In: THE EUROPEAN PHYSICAL JOURNAL PLUS. - ISSN 2190-5444. - 135:10(2020), pp. 853.1-853.30. [10.1140/epjp/s13360-020-00858-y]

Lagrangians and integrability for additive fourth-order difference equations

G. Gubbiotti
2020

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.
Settore MAT/07 - Fisica Matematica
   Discovery Projects - Grant ID: DP190101838
   Australian Research Council (ARC)
   Discovery Projects
   DP190101838

   Discovery Projects - Grant ID: DP200100210
   Australian Research Council (ARC)
   Discovery Projects
   DP200100210

   Geometric construction of critical solutions of nonlinear systems
   Australian Research Council (ARC)
   Australian Laureate Fellowships
   FL120100094
2020
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/946474
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