208 citations · 994 across the 36 of their papers we have counts for
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On linear degeneracy of integrable quasilinear systems in higher dimensions
E. V. Ferapontov, K. R. Khusnutdinova, C. Klein
We investigate -dimensional quasilinear systems which are integrable by the method of hydrodynamic reductions. In the case we formulate a conjecture that any such…
Double waves in multi-dimensional systems of hydrodynamic type: a necessary condition for integrability
E. V. Ferapontov, K. R. Khusnutdinova
An invariant differential-geometric approach to the integrability of (2+1)-dimensional systems of hydrodynamic type u_t+A(u)u_x+B(u)u_y=0 is developed. It is proved that the existe…
On a class of three-dimensional integrable Lagrangians
E. V. Ferapontov, K. R. Khusnutdinova, S. P. Tsarev
We characterize non-degenerate Lagrangians of the form such that the corresponding Euler-Lagrange equations $ (f_{u_x})_x+ (f_{u_y})_y+ (f_{u_t})…
Hydrodynamic reductions of multi-dimensional dispersionless PDEs: the test for integrability
E. V. Ferapontov, K. R. Khusnutdinova
A (d+1)-dimensional dispersionless PDE is said to be integrable if its n-component hydrodynamic reductions are locally parametrized by (d-1)n arbitrary functions of one variable. G…
The characterization of two-component (2+1)-dimensional integrable systems of hydrodynamic type
E. V. Ferapontov, K. R. Khusnutdinova
We obtain the necessary and sufficient conditions for a two-component (2+1)-dimensional system of hydrodynamic type to possess infinitely many hydrodynamic reductions. These condit…
On integrability of (2+1)-dimensional quasilinear systems
E. V. Ferapontov, K. R. Khusnutdinova
A (2+1)-dimensional quasilinear system is said to be `integrable' if it can be decoupled in infinitely many ways into a pair of compatible n-component one-dimensional systems in Ri…