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Register a new userIntegrable discretization of hodograph-type systems, hyperelliptic integrals and Whitham equations
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Added by
Boris Konopelchenko
Publication date
2014
fields
Physics
and research's language is
English
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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.
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