Dispersive deformations of hydrodynamic reductions of (2 + 1)D dispersionless integrable systems

Eugene Ferapontov, Antonio Moro

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)

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.
Original languageEnglish
Pages (from-to)035211
JournalJournal of Physics A: Mathematical and Theoretical
Volume42
Issue number3
DOIs
Publication statusPublished - 2008

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