Dispersive deformations of hydrodynamic reductions of 2D dispersionless integrable systems

Details Dispersive deformations of hydrodynamic reductions of 2D dispersionless integrable systems Dispersive deformations of hydrodynamic reductions of 2D dispersionless integrable systems

2008-07-15

arxiv.org/abs/0807.2409v3

J. Phys. A: Math. Theor, 42 No 3, pp. 035211 (1-15), 2009

Nonlinear Sciences

Exactly Solvable and Integrable Systems

18 pages, section added

Scientific paper

10.1088/1751-8113/42/3/035211

We demonstrate that hydrodynamic reductions of dispersionless integrable systems in 2+1 dimensions, such as the dispersionless Kadomtsev-Petviashvili (dKP) and dispersionless Toda lattice (dTl) equations, can be deformed into reductions of the corresponding dispersive counterparts. Modulo the Miura group, such deformations are unique. The requirement that any hydrodynamic reduction possesses a deformation of this kind imposes strong constraints on the structure of dispersive terms, suggesting an alternative approach to the integrability in 2+1 dimensions.

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