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Stationary Harry-Dym's equation and its relation with geodesics on ellipsoid

Authors:

Cao Cewen

Affiliation:

1. Department of Mathematics, Zhengzhou University, People's Republic of China

Abstract:

Harry-Dym's equation (HD) $r_tau = (r^{ - tfrac{1}{2}} )_{xxx}$ is well-known for its cusp soliton solutions. In this paper, relations are revealed between HD and a completely integrable Hamiltonian system in Liouville sense given by

$H = frac{1}{2}leftlangle {p,p} rightrangle - leftlangle {q,q} rightrangle ^{ - 1}$

Keywords:
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