Generalized Benney Lattice and the Heavenly Equation
Abstract
We generalize the Benney lattice and show that the new system of equations can be reduced to a generalized Chaplygin gas as well as the heavenly equation. We construct two infinite sets of conserved charges and show that one of the sets can be obtained from the Lax function. The conserved densities are related to Legendre polynomials and we present closed form expressions for the generating functions for these densities which also determines the Riemann invariants of the problem. We prove that the system is bi-Hamiltonian and that the conserved charges are in involution with respect to either of the Hamiltonian structures. We show that the associated generalized elastic medium equations are bi-Hamiltonian as well. We also bring out various other interesting features of our model.
Keywords
Cite
@article{arxiv.nlin/0204053,
title = {Generalized Benney Lattice and the Heavenly Equation},
author = {A. Constandache and Ashok Das and Ziemowit Popowicz},
journal= {arXiv preprint arXiv:nlin/0204053},
year = {2007}
}
Comments
10 pages