Integrability of differential–difference equations with discrete kinks

Ch. Scimiterna^ab, D. Levi<sup>ab

a</sup> INFN, Sezione di Roma Tre, Roma, Italy
^b Dipartimento di Ingegneria Elettronica, Università di Roma Tre, Roma, Italy

Abstract: We discuss a series of models introduced by Barashenkov, Oxtoby, and Pelinovsky to describe some discrete approximations of the $\phi^4$ theory that preserve traveling kink solutions. Using the multiple scale test, we show that they have some integrability properties because they pass the A$_1$ and A$_2$ conditions, but they are nonintegrable because they fail the A$_3$ conditions.

Keywords: lattice equation, kink solution, multiscale expansion, integrable equation.

Received: 23.06.2011

DOI: 10.4213/tmf6657

 English version: Theoretical and Mathematical Physics, 2011, 167:3, 826–842

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