Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 3 (2007), 096, 11 pages      arXiv:0706.0314

Lagrangian Approach to Dispersionless KdV Hierarchy

Amitava Choudhuri a, B. Talukdar a and U. Das b
a) Department of Physics, Visva-Bharati University, Santiniketan 731235, India
b) Abhedananda Mahavidyalaya, Sainthia 731234, India

Received June 05, 2007, in final form September 16, 2007; Published online September 30, 2007

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.

Key words: hierarchy of dispersionless KdV equations; Lagrangian approach; bi-Hamiltonian structure; variational symmetry.

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