Theoretical and Mathematical Physics

, Volume 167, Issue 3, pp 725–739

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


    • Novosibirsk State Technical University
  • A. V. Topovsky
    • Novosibirsk State Technical University
  • M. Yu. Basalaev
    • Novosibirsk State Technical University

DOI: 10.1007/s11232-011-0057-3

Cite this article as:
Dubrovsky, V.G., Topovsky, A.V. & Basalaev, M.Y. Theor Math Phys (2011) 167: 725. doi:10.1007/s11232-011-0057-3


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.


Nizhnik-Veselov-Novikov equationtwo-dimensional Kaup-Kupershmidt equationtwo-dimensional Sawada-Kotera equationsolutions with functional parameterstwo-dimensional stationary Schrödinger equationsolitontransparent potential
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© Pleiades Publishing, Ltd. 2011