This article is cited in 12 papers

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

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

Novosibirsk State Technical University, Novosibirsk, Russia

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.

Keywords: Nizhnik–Veselov–Novikov equation, two-dimensional Kaup–Kupershmidt equation, two-dimensional Sawada–Kotera equation, solutions with functional parameters, two-dimensional stationary Schrödinger equation, soliton, transparent potential.

Received: 23.06.2011

DOI: 10.4213/tmf6648

 English version: Theoretical and Mathematical Physics, 2011, 167:3, 725–739

Bibliographic databases:

• 
• 
• 
•