Abstract:
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.
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