Lagrangian Approach to Dispersionless KdV Hierarchy

Details Lagrangian Approach to Dispersionless KdV Hierarchy Lagrangian Approach to Dispersionless KdV Hierarchy

2007-06-03

arxiv.org/abs/0706.0314v3

SIGMA 3 (2007), 096, 11 pages

Nonlinear Sciences

Exactly Solvable and Integrable Systems

Published in SIGMA (Symmetry, Integrability and Geometry: Methods and pplications) at http://www.emis.de/journals/SIGMA/

Scientific paper

10.3842/SIGMA.2007.096

We derive a Lagrangian based approach to study the compatible Hamiltonian structure of the dispersionless KdV and supersymmetric KdV hierarchies and claim that our treatment of the problem serves as a very useful supplement of the so-called r-matrix method. We suggest specific ways to construct results for conserved densities and Hamiltonian operators. The Lagrangian formulation, via Noether's theorem, provides a method to make the relation between symmetries and conserved quantities more precise. We have exploited this fact to study the variational symmetries of the dispersionless KdV equation.

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