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Integrable discretization of hodograph-type systems, hyperelliptic integrals and Whitham equations | | B.G. Konopelchenko
; W.K. Schief
; | | Date: |
27 Nov 2014 | | Abstract: | Based on the well-established theory of discrete conjugate nets in discrete
differential geometry, we propose and examine discrete analogues of important
objects and notions in the theory of semi-Hamiltonian systems of hydrodynamic
type. In particular, we present discrete counterparts of (generalised)
hodograph equations, hyperelliptic integrals and associated cycles,
characteristic speeds of Whitham type and (implicitly) the corresponding
Whitham equations. By construction, the intimate relationship with integrable
system theory is maintained in the discrete setting. | | Source: | arXiv, 1411.7597 | | Services: | Forum | Review | PDF | Favorites | |
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