247 research outputs found
Gauge-invariant description of several (2+1)-dimensional integrable nonlinear evolution equations
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.Comment: Talk given at the Workshop "Nonlinear Physics: Theory and Experiment.
V", Gallipoli (Lecce, Italy), 12-21 June, 200
The Integrability of New Two-Component KdV Equation
We consider the bi-Hamiltonian representation of the two-component coupled
KdV equations discovered by Drinfel'd and Sokolov and rediscovered by Sakovich
and Foursov. Connection of this equation with the supersymmetric
Kadomtsev-Petviashvilli-Radul-Manin hierarchy is presented. For this new
supersymmetric equation the Lax representation and odd Hamiltonian structure is
given
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