Geodesic
Gauge-invariant description of several $(2+1)$-dimensional integrable nonlinear evolution equations
Teoretičeskaâ i matematičeskaâ fizika, Tome 160 (2009) no. 1, pp. 35-48

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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.
Mots-clés : Sawada–Kotera equation
Keywords: Kaup–Kuperschmidt equation, generalized dispersive long-wave equation, Davey–Stewartson equation, Nizhnik–Veselov–Novikov equation. 
@article{TMF_2009_160_1_a3,
     author = {V. G. Dubrovskii and A. V. Gramolin},
     title = {Gauge-invariant description of several $(2+1)$-dimensional integrable nonlinear evolution equations},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {35--48},
     publisher = {mathdoc},
     volume = {160},
     number = {1},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2009_160_1_a3/}
}
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V. G. Dubrovskii; A. V. Gramolin. Gauge-invariant description of several $(2+1)$-dimensional integrable nonlinear evolution equations. Teoretičeskaâ i matematičeskaâ fizika, Tome 160 (2009) no. 1, pp. 35-48. http://geodesic.mathdoc.fr/item/TMF_2009_160_1_a3/