"A coordinate-free construction of conservation laws and reciprocal transformations for a class of integrable hydrodynamic-type systems"@en . "000271406300023" . "Using a (1, 1)-tensor L with zero Nijenhuis torsion and maximal possible number (equal to the number of dependent variables) of distinct, functionally independent eigenvalues we define, in a coordinate-free fashion, the seed systems which are weakly nonlinear semi-Hamiltonian systems of a special form, and an infinite set of conservation laws for the seed systems. The reciprocal transformations constructed from these conservation laws yield a considerably larger class of hydrodynamic-type systems from the seed systems, and we show that these new systems are again defined in a coordinate-free manner, using the tensor L alone, and, moreover, are weakly nonlinear and semi-Hamiltonian, so their general solution can be obtained by means of the generalized hodograph method of Tsarev." . . . "B\u0142aszak, Maciej" . "GB - Spojen\u00E9 kr\u00E1lovstv\u00ED Velk\u00E9 Brit\u00E1nie a Severn\u00EDho Irska" . "Z(MSM4781305904)" . "64" . . . "A coordinate-free construction of conservation laws and reciprocal transformations for a class of integrable hydrodynamic-type systems" . . . . "Reports on Mathematical Physics" . "2"^^ . . . "A coordinate-free construction of conservation laws and reciprocal transformations for a class of integrable hydrodynamic-type systems"@en . . "RIV/47813059:19610/09:#0000273" . . "1-2" . "A coordinate-free construction of conservation laws and reciprocal transformations for a class of integrable hydrodynamic-type systems" . . "2"^^ . . . "B\u0142aszak, Maciej" . "RIV/47813059:19610/09:#0000273!RIV10-MSM-19610___" . "Sergyeyev, Artur" . . . . "14"^^ . . "L-tensor; Killing tensor; dispersionless integrable systems; reciprocal transformations; weakly nonlinear semi-Hamiltonian hydrodynamic-type systems; generalized hodograph method; conservation laws; Riemann invariants"@en . "0034-4877" . . "[6CAAC4C83451]" . "301221" . "19610" . . "Using a (1, 1)-tensor L with zero Nijenhuis torsion and maximal possible number (equal to the number of dependent variables) of distinct, functionally independent eigenvalues we define, in a coordinate-free fashion, the seed systems which are weakly nonlinear semi-Hamiltonian systems of a special form, and an infinite set of conservation laws for the seed systems. The reciprocal transformations constructed from these conservation laws yield a considerably larger class of hydrodynamic-type systems from the seed systems, and we show that these new systems are again defined in a coordinate-free manner, using the tensor L alone, and, moreover, are weakly nonlinear and semi-Hamiltonian, so their general solution can be obtained by means of the generalized hodograph method of Tsarev."@en .