Critical points, Lauricella functions and Whitham-type equations
Exactly Solvable and Integrable Systems
2015-06-11 v1 Mathematical Physics
Differential Geometry
math.MP
Abstract
A large class of semi-Hamiltonian systems of hydrodynamic type is interpreted as the equations governing families of critical points of functions obeying the classical linear Darboux equations for conjugate nets.The distinguished role of the Euler-Poisson-Darboux equations and associated Lauricella-type functions is emphasised. In particular, it is shown that the classical g-phase Whitham equations for the KdV and NLS equations are obtained via a g-fold iterated Darboux-type transformation generated by appropriate Lauricella functions.
Cite
@article{arxiv.1411.5856,
title = {Critical points, Lauricella functions and Whitham-type equations},
author = {Y. Kodama and B. Konopelchenko and W. K. Schief},
journal= {arXiv preprint arXiv:1411.5856},
year = {2015}
}
Comments
14 pages