This article is cited in 5 papers

Gauge-invariant description of several $(2+1)$-dimensional integrable nonlinear evolution equations

V. G. Dubrovskii, A. V. Gramolin

Novosibirsk State Technical University

Abstract: We obtain new gauge-invariant forms of two-dimensional integrable systems of nonlinear equations: the Sawada–Kotera and Kaup–Kuperschmidt system, the generalized system of dispersive long waves, and the Nizhnik–Veselov–Novikov system. We show how these forms imply both new and well-known two-dimensional integrable nonlinear equations: the Sawada–Kotera equation, Kaup–Kuperschmidt equation, dispersive long-wave system, Nizhnik–Veselov–Novikov equation, and modified Nizhnik–Veselov–Novikov equation. We consider Miura-type transformations between nonlinear equations in different gauges.

Keywords: Sawada–Kotera equation, Kaup–Kuperschmidt equation, generalized dispersive long-wave equation, Davey–Stewartson equation, Nizhnik–Veselov–Novikov equation.

DOI: 10.4213/tmf6376

 English version: Theoretical and Mathematical Physics, 2009, 160:1, 905–916

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