This article is cited in 9 papers

On a nonlinear integrable difference equation on the square

D. Levi^ab, R. I. Yamilov<sup>c

a</sup> Sezione INFN
^b Dipartimento di Ingegneria Elettronica, Università degli Studi Roma Tre
^c Ufa Institute of Mathematics, Russian Academy of Sciences

Abstract: 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 differential-difference equations. This equation is not symmetric with respect to the exchange of the two discrete variables. Its integrability is proved by constructing its Lax pair.

Keywords: nonlinear integrable difference equation, Lax pair, Miura transformation, Volterra equation.

UDC: 517.9

Received: 27.04.2009

Language: English

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