Integrability properties of the dispersionless Kadomtsev-Petviashvili hierarchy
Abstract
In the paper we investigate integrability characteristics for the dispersionless Kadomtsev-Petviashvili hierarchy. These characteristics include symmetries, Hamiltonian structures and conserved quantities. We give a Lax triad to construct a master symmetry and a hierarchy of non-isospectral dispersionless Kadomtsev-Petviashvili flows. These non-isospectral flows, together with the known isospectral dispersionless Kadomtsev-Petviashvili flows, form a Lie algebra, which is used to derive two sets of symmetries for the isospectral dispersionless Kadomtsev-Petviashvili hierarchy. By means of the master symmetry, symmetries, Noether operator and conserved covariants, Hamiltonian structures are constructed for both isospectral and non-isospectral dispersionless Kadomtsev-Petviashvili hierarchies. Finally, two sets of conserved quantities and their Lie algebra are derived for the isospectral dispersionless Kadomtsev-Petviashvili hierarchy.
Keywords
Cite
@article{arxiv.1312.7174,
title = {Integrability properties of the dispersionless Kadomtsev-Petviashvili hierarchy},
author = {Wei Fu and R. Ilangovane and K. M. Tamizhmani and Da-jun Zhang},
journal= {arXiv preprint arXiv:1312.7174},
year = {2014}
}