Dispersive deformations of hydrodynamic reductions of 2D dispersionless integrable systems

Abstract

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.

18 pages, section added

References in corpus (3)

• Algebro-geometric approach in the theory of integrable hydrodynamic type systems
• Hamiltonian systems of hydrodynamic type in 2 + 1 dimensions
• Multidimensional integrable systems and deformations of Lie algebra homomorphisms

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• Gardner's deformations as generators of new integrable systems