Geodesic
New exact solutions of two-dimensional integrable equations using the $\bar\partial$-dressing method
Teoretičeskaâ i matematičeskaâ fizika, Tome 167 (2011) no. 3, pp. 377-393 Cet article a éte moissonné depuis la source Math-Net.Ru

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We review new classes of exact solutions with functional parameters with constant asymptotic values at infinity of the Nizhnik–Veselov–Novikov equation and new classes of exact solutions with functional parameters of two-dimensional generalizations of the Kaup–Kupershmidt and Sawada–Kotera equations, constructed using the Zakharov–Manakov $\bar\partial$-dressing method. We present subclasses of multisoliton and periodic solutions of these equations and give examples of linear superpositions of exact solutions of the Nizhnik–Veselov–Novikov equation.
Keywords: Nizhnik–Veselov–Novikov equation, two-dimensional Kaup–Kupershmidt equation, two-dimensional Sawada–Kotera equation, solutions with functional parameters, two-dimensional stationary Schrödinger equation, transparent potential.
Mots-clés : soliton 
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V. G. Dubrovsky; A. V. Topovsky; M. Yu. Basalaev. New exact solutions of two-dimensional integrable equations using the $\bar\partial$-dressing method. Teoretičeskaâ i matematičeskaâ fizika, Tome 167 (2011) no. 3, pp. 377-393. http://geodesic.mathdoc.fr/item/TMF_2011_167_3_a4/

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