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Integrability of differential-difference equations with discrete kinks

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Abstract

We discuss a series of models introduced by Barashenkov, Oxtoby, and Pelinovsky to describe some discrete approximations of the Φ4 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.

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Authors and Affiliations

  1. Dipartimento di Ingegneria Elettronica, Università di Roma Tre and INFN, Sezione di Roma Tre, Rome, Italy

    C. Scimiterna & D. Levi

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  1. C. Scimiterna
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  2. D. Levi
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Correspondence to C. Scimiterna.

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Prepared from an English manuscript submitted by the authors; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 167, No. 3, pp. 496–513, June, 2011.

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Scimiterna, C., Levi, D. Integrability of differential-difference equations with discrete kinks. Theor Math Phys 167, 826–842 (2011). https://doi.org/10.1007/s11232-011-0066-2

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