M. B. Sheftel, "Symmetry group analysis and invariant solutions of hydrodynamic-type systems", International Journal of Mathematics and Mathematical Sciences, vol. 2004, Article ID 472053, 48 pages, 2004. https://doi.org/10.1155/S0161171204206147
Symmetry group analysis and invariant solutions of hydrodynamic-type systems
We study point and higher symmetries of systems of the hydrodynamic type with and without an explicit dependence on . We consider such systems which satisfy the existence conditions for an infinite-dimensional group of hydrodynamic symmetries which implies linearizing transformations for these systems. Under additional restrictions on the systems, we obtain recursion operators for symmetries and use them to construct infinite discrete sets of exact solutions of the studied equations. We find the interrelation between higher symmetries and recursion operators. Two-component systems are studied in more detail than -component systems. As a special case, we consider Hamiltonian and semi-Hamiltonian systems of Tsarëv.
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