116 citations · 762 across the 46 of their papers we have counts for
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The Kundu--Eckhaus equation and its discretizations
Decio Levi, Christian Scimiterna
In this article we show that the complex Burgers and the Kundu--Eckhaus equations are related by a Miura transformation. We use this relation to discretize the Kundu--Eckhaus equat…
Multiscale reduction of discrete nonlinear Schroedinger equations
D. Levi, M. Petrera, C. Scimiterna
We use a discrete multiscale analysis to study the asymptotic integrability of differential-difference equations. In particular, we show that multiscale perturbation techniques pro…
The Generalized Symmetry Method for Discrete Equations
D. Levi, R. I. Yamilov
The generalized symmetry method is applied to a class of completely discrete equations including the Adler-Bobenko-Suris list. Assuming the existence of a generalized symmetry, we…
On a nonlinear integrable difference equation on the square 3D-inconsistent
D. Levi, R. I. Yamilov
We present a nonlinear partial difference equation defined on a square which is obtained by combining the Miura transformations between the Volterra and the modified Volterra diffe…