] o c n m p [Open Communications in Nonlinear Mathematical Physics |
Rafael Hernandez Heredero ; Decio Levi ; Christian Scimiterna - High order multiscale analysis of discrete integrable equations
ocnmp:11690 - Open Communications in Nonlinear Mathematical Physics, February 15, 2024, Special Issue in Memory of Decio Levi - https://doi.org/10.46298/ocnmp.11690High order multiscale analysis of discrete integrable equationsArticle
Authors: Rafael Hernandez Heredero 
1; Decio Levi 2; Christian Scimiterna 3
- 1 Universidad Politécnica de Madrid
- 2 Università degli Studi Roma Tre = Roma Tre University
- 3 Istituto di Istruzione Superiore Sansi-Leonardi-Volta, Spoleto
In this article we present the results obtained applying the multiple scale expansion up to the order $\varepsilon^6$ to a dispersive multilinear class of equations on a square lattice depending on 13 parameters. We show that the integrability conditions given by the multiple scale expansion give rise to 4 nonlinear equations, 3 of which seem to be new, depending at most on 2 parameters.
Source: HAL:hal-04173064v3
Volume: Special Issue in Memory of Decio Levi
Published on: February 15, 2024
Accepted on: October 6, 2023
Submitted on: August 2, 2023
Keywords: Multiple Scale,Integrable Difference Equations,PACS: 02.30.Ks, 02.30.Ik, 02.30.MvMSC 4E13, 37K10, 39A14, 93B18,[NLIN.NLIN-SI]Nonlinear Sciences [physics]/Exactly Solvable and Integrable Systems [nlin.SI],[MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph]
Classifications
Mathematics Subject Classification 20201
- 34-XX - Ordinary differential equations
- 34E13 - Multiple scale methods for ordinary differential equations
- 37-XX - Dynamical systems and ergodic theory
- 39A12 - Discrete version of topics in analysis
- 39A14 - Partial difference equations
- 39A36 - Integrable difference and lattice equations; integrability tests
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