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SIGMA 3 (2007), 096, 11 pages arXiv:0706.0314
https://doi.org/10.3842/SIGMA.2007.096
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
Abstract
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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