, Volume 167, Issue 3, pp 725-739
Date: 09 Jul 2011

New exact solutions of two-dimensional integrable equations using the \(\bar \partial \) -dressing method

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Abstract

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.

Prepared from an English manuscript submitted by the authors; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 167, No. 3, pp. 377–393, June, 2011.