New exact solutions of two-dimensional integrable equations using the \(\bar \partial \)-dressing method
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- Dubrovsky, V.G., Topovsky, A.V. & Basalaev, M.Y. Theor Math Phys (2011) 167: 725. doi:10.1007/s11232-011-0057-3
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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.