## Lagrangian approach to dispersionless KdV hierarchy

### Summary

Summary: 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.

### Mathematics Subject Classification

35A15, 37K05, 37K10

### Keywords/Phrases

hierarchy of dispersionless KdV equations, Lagrangian approach, bi-Hamiltonian structure, variational symmetry