Symmetry constraints for dispersionless integrable equations and systems of hydrodynamic type

Abstract

Symmetry constraints for (2+1)-dimensional dispersionless integrable equations are considered. It is demonstrated that they naturally lead to systems of hydrodynamic type which arise within the reduction method. One also easily obtaines an associated complex curve (Sato function) and corresponding generating equations. Dispersionless KP and 2DTL hierarchy are considered as illustrative examples.

16 pages, LaTeX

References in corpus (5)

• On integrability of (2+1)-dimensional quasilinear systems
• The characterization of two-component (2+1)-dimensional integrable systems of hydrodynamic type
• Boyer-Finley equation and systems of hydrodynamic type
• A hodograph transformation which applies to the heavenly equation
• Nonlinear Beltrami equation and tau-function for dispersionless hierarchies

Cited by in corpus (25)

• The characterization of two-component (2+1)-dimensional integrable systems of hydrodynamic type
• Light propagation in a Cole-Cole nonlinear medium via Burgers-Hopf equation
• On the dbar-dressing method applicable to heavenly equation
• Integrable equations in nonlinear geometrical optics
• Algebro-geometric approach in the theory of integrable hydrodynamic type systems
• Classification of integrable hydrodynamic chains and generating functions of conservation laws
• The Hamiltonian approach in classification and integrability of hydrodynamic chains
• On the heavenly equation hierarchy and its reductions
• On a class of reductions of Manakov-Santini hierarchy connected with the interpolating system
• Integrability of the Manakov--Santini hierarchy
• Explicit solutions of the WDVV equation determined by the "flat" hydrodynamic reductions of the Egorov hydrodynamic chains
• A dispersionless integrable system associated to Diff$(S^1)$ gauge theory
• The quasiclassical limit of the symmetry constraint of the KP hierarchy and the dispersionless KP hierarchy with self-consistent sources
• On the water-bag model of dispersionless KP hierarchy (II)
• On the water-bag model of dispersionless KP hierarchy
• The Kupershmidt hydrodynamic chains and lattices
• Logarithmic deformations of the rational superpotential/Landau-Ginzburg construction of solutions of the WDVV equations
• Hydrodynamic Reductions of Dispersionless Harry Dym Hierarchy
• Dispersionless BKP equation, the Manakov-Santini system and Einstein-Weyl structures
• Remarks on the waterbag model of dispersionless Toda Hierarchy
• Integrable hydrodynamic chains associated with Dorfman Poisson brackets
• Transformations of integrable hydrodynamic chains and their hydrodynamic reductions
• Integrable systems of the intermediate long wave type in 2+1 dimensions
• Old and New Reductions of Dispersionless Toda Hierarchy
• Solutions for real dispersionless Veselov-Novikov hierarchy