Integrability of the Gibbons–Tsarev system
نویسنده
چکیده
A new approach extracting multi-parametric hydrodynamic reductions for the integrable hydrodynamic chains is presented. The Benney hydrodynamic chain is considered.
منابع مشابه
Integrability of the Egorov hydrodynamic type systems
Integrability criterion for the Egorov hydrodynamic type systems is presented. The general solution by the generalized hodograph method is found. Examples are given. A description of three orthogonal curvilinear coordinate nets is discussed from the viewpoint of reciprocal transformations. In honour of Sergey Tsarev
متن کاملHyperdeterminants as integrable discrete systems
We give the basic definitions and some theoretical results about hyperdeterminants, introduced by A. Cayley in 1845. We prove integrability (understood as 4d-consistency) of a nonlinear difference equation defined by the 2×2×2 hyperdeterminant. This result gives rise to the following hypothesis: the difference equations defined by hyperdeterminants of any size are integrable. We show that this ...
متن کاملHYDRODYNAMIC TYPE SYSTEMS AND THEIR INTEGRABILITY Introduction for Applied Mathematicians
Hydrodynamic type systems are systems of quasilinear equations of the first order. They naturally arise in continuum mechanics but also occur as a result of semi-classical approximations of nonlinear dispersive waves. The mathematical theory of one-dimensional hyperbolic quasilinear equations initiated by B. Riemann in XIX century has been developed into a rich and diverse area of applied mathe...
متن کاملOld and New Reductions of Dispersionless Toda Hierarchy
This paper is focused on geometric aspects of two particular types of finitevariable reductions in the dispersionless Toda hierarchy. The reductions are formulated in terms of “Landau–Ginzburg potentials” that play the role of reduced Lax functions. One of them is a generalization of Dubrovin and Zhang’s trigonometric polynomial. The other is a transcendental function, the logarithm of which re...
متن کاملDifferential Geometry of Strongly Integrable Systems of Hydrodynamic Type
Here the matrix (gij) (assumed nondegenerate) defines a pseudo-Riemannian metric (with upper indices) of zero curvature on the u-space, Fjk i = Fjki(u) being the corresponding Levi-Civita connection. Thus, the integrability condition can be formulated in terms of the differential geometry of SHT. For such integrable systems S. P. Tsarev [3] found a generalization (for N _> 3) of the hodograph m...
متن کامل