Geodesic
Hamiltonian formalism of weakly nonlinear hydrodynamic systems
Teoretičeskaâ i matematičeskaâ fizika, Tome 73 (1987) no. 2, pp. 316-320

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Systems of quasilinear equations are considered which are diagonalizable and Hamiltonian, with the condition $\partial_iv^i=0$ where $u_t^i=v^i(u)u_x^i$, $i=1,\dots,N$. Conservation laws of such systems are found as well as metrics and Poisson brackets. By concrete examples the procedure of finding the solutions is demonstrated. Conditions of the existence of solutions and continuity of commuting flows are pointed out. 
@article{TMF_1987_73_2_a15,
     author = {M. V. Pavlov},
     title = {Hamiltonian formalism of weakly nonlinear hydrodynamic systems},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {316--320},
     publisher = {mathdoc},
     volume = {73},
     number = {2},
     year = {1987},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1987_73_2_a15/}
}
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M. V. Pavlov. Hamiltonian formalism of weakly nonlinear hydrodynamic systems. Teoretičeskaâ i matematičeskaâ fizika, Tome 73 (1987) no. 2, pp. 316-320. http://geodesic.mathdoc.fr/item/TMF_1987_73_2_a15/