Pavlov, M. V. Conservation of the ”forms” of Hamiltonian structures upon linear substitution for independent variables. (English. Russian original) Zbl 0848.35133 Math. Notes 57, No. 5, 489-495 (1995); translation from Mat. Zametki 57, No. 5, 704-711 (1995). For several multidimensional Hamiltonian systems it is proved that after any linear changes of independent variables they have the same “form”. Reviewer: M.Perelmuter (Kiev) Cited in 9 Documents MSC: 35Q72 Other PDE from mechanics (MSC2000) 37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests 37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) Keywords:multidimensional Hamiltonian systems; linear changes of independent variables PDFBibTeX XMLCite \textit{M. V. Pavlov}, Math. Notes 57, No. 5, 704--711 (1995; Zbl 0848.35133); translation from Mat. Zametki 57, No. 5, 704--711 (1995) Full Text: DOI References: [1] S. P. Tsarev, ”The Hamiltonian property of stationary and inverse equations of mechanics,” Mat. Zametki,46, No. 1, 105–111 (1989). · Zbl 0734.35106 [2] O. I. Mokhov, ”On the Hamiltonian structure of evolution with respect to spatial variables,” Usp. Mat. Nauk.,45, No. 1, 181–182 (1990). [3] S. P. Tsarev, ”The geometry of Hamiltonian systems of hydrodynamic type,” Izv. Akad. Nauk SSSR, Ser. Mat.,54, 1048–1068 (1990). [4] S. P. Tsarev, Differential-Geometric Methods for Integration of Hydrodynamic Type [in Russian], Doctoral Dissertation, MIAN, Moscow (1993). · Zbl 0795.35121 [5] B. A. Dubrovin and S. P. Novikov, ”The Hamiltonian formalism for one-dimensional systems of hydrodynamic type,” Dokl. Akad. Nauk SSSR,270, No. 4, 781–785 (1983). · Zbl 0553.35011 [6] V. E. Zakharov and E. A. Kuznetsov, ”Hamiltonian formalism for systems of hydrodynamic type,” Math. Soviet Review,4 (1982). · Zbl 0557.76008 [7] L. D. Landau and E. M. Lifschitz, The Electrodynamics of Solids [in Russian], Nauka, Moscow (1982). [8] A. V. Gurevich, A. L. Krylov, V. V. Khodorovskii, and G. A. El’, ”Supersonic flow about a body in dispersional hydrodynamics,” Zh. Eksp. Teor. Fiz., (1994). This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.