https://doi.org/10.1140/epjp/s13360-020-00858-y
Regular Article
Lagrangians and integrability for additive fourth-order difference equations
School of Mathematics and Statistics F07, The University of Sydney, 2006, Sydney, NSW, Australia
a
giorgio.gubbiotti@sydney.edu.au
Received:
12
February
2020
Accepted:
11
October
2020
Published online:
20
October
2020
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.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2020
