Hamiltonian Structures for the Generalized Dispersionless KdV Hierarchy

  title={Hamiltonian Structures for the Generalized Dispersionless KdV Hierarchy},
  author={J. C. Brunelli},
  journal={Reviews in Mathematical Physics},
  • J. C. Brunelli
  • Published 5 January 1996
  • Mathematics, Physics
  • Reviews in Mathematical Physics
We study from a Hamiltonian point of view the generalized dispersionless KdV hierarchy of equations. From the so-called dispersionless Lax representation of these equations we obtain three compatible Hamiltonian structures. The second and third Hamiltonian structures are calculated directly from the r-matrix approach. Since the third structure is not related recursively with the first two the generalized dispersionless KdV hierarchy can be characterized as a truly tri-Hamiltonian system. 
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Hamiltonian methods in the theory of solitons
The Nonlinear Schrodinger Equation (NS Model).- Zero Curvature Representation.- The Riemann Problem.- The Hamiltonian Formulation.- General Theory of Integrable Evolution Equations.- Basic Examples
Elements of the theory of representations
First Part. Preliminary Facts.- 1. Sets, Categories, Topology.- 1.1. Sets.- 1.2. Categories and Functors.- 1.3. The Elements of Topology.- 2. Groups and Homogeneous Spaces.- 2.1. Transformation
Mod. Phys. Lett. A9
  • Mod. Phys. Lett. A9
  • 1994
I. Krichever, Commun. Math. Phys
  • I. Krichever, Commun. Math. Phys
  • 1992
J. Math. Phys
  • J. Math. Phys
  • 1992
Comm. Math. Phys
  • Comm. Math. Phys
  • 1989
J. Math. Phys
  • J. Math. Phys
  • 1988
Comm. Math. Phys
  • Comm. Math. Phys
  • 1985
J. Sov. Math
  • J. Sov. Math
  • 1985