• Corpus ID: 373482

Integrability of the Egorov hydrodynamic type systems

@article{Pavlov2006IntegrabilityOT,
  title={Integrability of the Egorov hydrodynamic type systems},
  author={Maxim V. Pavlov},
  journal={arXiv: Exactly Solvable and Integrable Systems},
  year={2006}
}
  • M. Pavlov
  • Published 6 June 2006
  • Mathematics
  • arXiv: Exactly Solvable and Integrable Systems
Integrability criterion for the Egorov hydrodynamic type systems is presented. The general solution by generalized hodograph method is found. Examples are given 
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5 Citations
Background Citations
2
Methods Citations
2

5 Citations

Citation Type

Citation Type

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References

SHOWING 1-10 OF 62 REFERENCES
THE GEOMETRY OF HAMILTONIAN SYSTEMS OF HYDRODYNAMIC TYPE. THE GENERALIZED HODOGRAPH METHOD
It is proved that there exists an infinite involutive family of integrals of hydrodynamic type for diagonal Hamiltonian systems of quasilinear equations; the completeness of the family is also…
Tri-Hamiltonian Structures of Egorov Systems of Hydrodynamic Type
We prove a simple condition under which the metric corresponding to a diagonalizable semi-Hamiltonian hydrodynamic type system belongs to the class of Egorov (potential) metrics. For Egorov diagonal…
A method for solving the dispersionless KP hierarchy and its exact solutions. II
Description of the $n$-orthogonal curvilinear coordinate systems and Hamiltonian integrable systems of hydrodynamic type, I: Integration of the Lamé equations
The classical problem of description of n-Orthogonal Curvilinear Coordinate System in flat Euclidean space is solved by the Inverse Scattering Method. The developed method allows to describe…
The Generating Formula for The Solutions to The Associativity Equations
An exact formula for the solutions to the WDVV equation in terms of horizontal sections of the corresponding flat connection is found.
Hydrodynamic reductions of the heavenly equation
We demonstrate that Plebanski's first heavenly equation decouples in infinitely many ways into a triple of commuting (1 + 1)-dimensional systems of hydrodynamic type which satisfy the Egorov…
Classification of Integrable (2+1)-Dimensional Quasilinear Hierarchies
We investigate the (2+1)-dimensional hierarchies associated with the integrable PDEs of the form Δ tt = F(Δxx, Δxt, Δxy), which generalize the dispersionless KP hierarchy. Integrability is understood…
Dressing methods for geometric nets: II. Orthogonal and Egorov nets
The Grassmannian formalism of KP hierarchies is used to study geometric nets of orthogonal type and their subclass of Egorov nets. Efficient dressing methods for Cauchy propagators are provided which…
Integrable systems in topological field theory
Equations of Associativity in Two-Dimensional Topological Field Theory as Integrable Hamiltonian Nondiagonalizable Systems of Hydrodynamic Type
Equations of associativity in two-dimensional topological field theory (they are known also as the Witten-Dijkgraaf-H.Verlinde-E.Verlinde (WDVV) system) are represented as an example of the general…
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