Lagrangian Approach to Dispersionless KdV Hierarchy
Copyright policy )Lagrangian Approach to Dispersionless KdV Hierarchy
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.
Published in SIGMA (Symmetry, Integrability and Geometry: Methods and pplications) at http://www.emis.de/journals/SIGMA/
- Visva-Bharati University India
Nonlinear Sciences - Exactly Solvable and Integrable Systems, hierarchy of dispersionless KdV equations, Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.), FOS: Physical sciences, variational symmetry, bi-Hamiltonian structure, Variational methods applied to PDEs, KdV equations (Korteweg-de Vries equations), Lagrangian approach, QA1-939, Exactly Solvable and Integrable Systems (nlin.SI), Hamiltonian structures, symmetries, variational principles, conservation laws, Mathematics
Nonlinear Sciences - Exactly Solvable and Integrable Systems, hierarchy of dispersionless KdV equations, Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.), FOS: Physical sciences, variational symmetry, bi-Hamiltonian structure, Variational methods applied to PDEs, KdV equations (Korteweg-de Vries equations), Lagrangian approach, QA1-939, Exactly Solvable and Integrable Systems (nlin.SI), Hamiltonian structures, symmetries, variational principles, conservation laws, Mathematics
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