Linearly Degenerate Reducible Systems of Hydrodynamic Type
@article{Agafonov1998LinearlyDR,
title={Linearly Degenerate Reducible Systems of Hydrodynamic Type},
author={Sergey I. Agafonov},
journal={Journal of Mathematical Analysis and Applications},
year={1998},
volume={222},
pages={15-37}
}Abstract We propose a complete description and classification of 3 × 3 linearly degenerate reducible systems of hydrodynamic type and show that any strictly hyperbolic system of this class can be reduced to the scalar Monge–Ampere type equation of the 3 d order.
13 Citations
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References
SHOWING 1-7 OF 7 REFERENCES
Dupin hypersurfaces and integrable hamiltonian systems of hydrodynamic type, which do not possess Riemann invariants
- Mathematics
- 1995
On integrability of 3x3 semi-Hamiltonian hydrodynamic type systems u t i =v i j (u)u x j which do not possess Riemann in variants
- Mathematics
- 1993
Exceptionality Condition and Linearization Procedure for a Third Order Nonlinear PDE
- Mathematics
- 1994
Abstract We determine a third order hyperbolic nonlinear partial differential equation possessing the property of being completely exceptional; i.e., every admissible discontinuity wave never evolves…
On the matrix Hopf equation and integrable Hamiltonian systems of hydrodynamic type, which do not possess Riemann invariants
- Mathematics
- 1993
Geometry of 2D topological field theories
- Mathematics, Physics
- 1994
These lecture notes are devoted to the theory of “equations of associativity” describing geometry of moduli spaces of 2D topological field theories.
Sur l'équation générale de Monge-Ampère d'ordre supérieur
- Mathematics
- 1992
L'equation de Monge-Ampere d'ordre pair, caracterisee par l'exceptionnalite de ses surfaces d'onde, s'obtient en annulant une fonction lineaire d'un determinant de Hankel et de ses mineurs de tous…