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

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

2009-07-20

arxiv.org/abs/0907.3205v1

Theor. Math. Phys. 160 (2009) 905

Nonlinear Sciences

Exactly Solvable and Integrable Systems

Talk given at the Workshop "Nonlinear Physics: Theory and Experiment. V", Gallipoli (Lecce, Italy), 12-21 June, 2008

Scientific paper

10.1007/s11232-009-0080-9

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.

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