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- Decio Levi, Matteo Petrera, C. SCIMITERNA

We present a discrete multiscale expansion of the lattice potential Korteweg-de Vries (lpKdV) equation on functions of infinite order of slow-varyness. To do so we introduce a formal expansion of theâ€¦ (More)

- Decio Levi, Matteo Petrera, Christian SCIMITERNA, Ravil YAMILOV
- 2008

We construct Miura transformations mapping the scalar spectral problems of the integrable lattice equations belonging to the Adlerâ€“Bobenkoâ€“Suris (ABS) list into the discrete SchrÃ¶dinger spectralâ€¦ (More)

We discuss umbral calculus as a method of systematically discretizing linear differential equations while preserving their point symmetries as well as generalized symmetries. The method is thenâ€¦ (More)

Lie group theory was originally created more than 100 years ago as a tool for solving ordinary and partial differential equations. In this article we review the results of a much more recent program:â€¦ (More)

- Decio Levi
- 2007

In this paper we present a set of results on the integration and on the symmetries of the lattice potential Korteweg-de Vries (lpKdV) equation. Using its associated spectral problem we construct theâ€¦ (More)

- Decio Levi, Matteo Petrera
- 2006

We expand a partial difference equation (Pâˆ†E) on multiple lattices and obtain the Pâˆ†E which governs its far field behaviour. The perturbativeâ€“reductive approach is here performed on well knownâ€¦ (More)

- Decio Levi
- 2008

Multiple-scale analysis of discrete nonlinear partial difference equations: the reduction of the lattice potential KdV. Abstract We consider multiple lattices and functions defined on them. Weâ€¦ (More)

- R. HERNANDEZ HEREDERO, Decio Levi, Matteo Petrera, C. SCIMITERNA
- 2008

We conjecture an integrability and linearizability test for dispersive Z-lattice equations by using a discrete multiscale analysis. The lowest order secularity conditions from the multiscaleâ€¦ (More)

- R HernÃ¡ndez Heredero, Decio Levi, C Scimiterna
- 2010

In this paper we consider the classification of dispersive linearizable partial difference equations defined on a quad-graph by the mÃºltiple scale reduction around their harmonic solution. We showâ€¦ (More)

- Christian SCIMITERNA, Decio Levi
- 2010

In this paper we are extending the well known integrability theorems obtained by multiple scale techniques to the case of linearizable difference equations. As an example we apply the theory to theâ€¦ (More)