Geodesic
Integrability of differential--difference equations with discrete kinks
Teoretičeskaâ i matematičeskaâ fizika, Tome 167 (2011) no. 3, pp. 496-513

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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, integrable equation.
Mots-clés : multiscale expansion 
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     author = {Ch. Scimiterna and D. Levi},
     title = {Integrability of differential--difference equations with discrete kinks},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {496--513},
     publisher = {mathdoc},
     volume = {167},
     number = {3},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2011_167_3_a13/}
}
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Ch. Scimiterna; D. Levi. Integrability of differential--difference equations with discrete kinks. Teoretičeskaâ i matematičeskaâ fizika, Tome 167 (2011) no. 3, pp. 496-513. http://geodesic.mathdoc.fr/item/TMF_2011_167_3_a13/