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Teoreticheskaya i Matematicheskaya Fizika, 2011, Volume 167, Number 3, Pages 496–513
DOI: https://doi.org/10.4213/tmf6657 (Mi tmf6657) 		 
Integrability of differential–difference equations with discrete kinks

Ch. Scimiternaab, D. Leviab

a INFN, Sezione di Roma Tre, Roma, Italy
b Dipartimento di Ingegneria Elettronica, Università di Roma Tre, Roma, Italy
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DOI: https://doi.org/10.4213/tmf6657
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
English version:
Theoretical and Mathematical Physics, 2011, Volume 167, Issue 3, Pages 826–842
DOI: https://doi.org/10.1007/s11232-011-0066-2
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Document Type: Article
Language: Russian
Citation: Ch. Scimiterna, D. Levi, “Integrability of differential–difference equations with discrete kinks”, TMF, 167:3 (2011), 496–513; Theoret. and Math. Phys., 167:3 (2011), 826–842
Citation in format AMSBIB
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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