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

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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.

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Authors and Affiliations

  1. Novosibirsk State Technical University, Novosibirsk, Russia

    V. G. Dubrovsky, A. V. Topovsky & M. Yu. Basalaev

Authors
  1. V. G. Dubrovsky
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  2. A. V. Topovsky
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  3. M. Yu. Basalaev
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Correspondence to V. G. Dubrovsky.

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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.

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Dubrovsky, V.G., Topovsky, A.V. & Basalaev, M.Y. New exact solutions of two-dimensional integrable equations using the \(\bar \partial \)-dressing method. Theor Math Phys 167, 725–739 (2011). https://doi.org/10.1007/s11232-011-0057-3

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