= Classical integrability
{title2=$\{I_j,I_k\}=0$}
For a finite-dimensional <Hamiltonian system>, integrability is normally expressed by enough independent first integrals in mutual <Poisson bracket> involution. In classical field theories, an infinite hierarchy of compatible <conserved quantities> is the corresponding structure. For <Sine-Gordon theory>, <Bäcklund transformations> generate local <conservation laws> and explicit soliton solutions. Conservation of arbitrary quantities alone should not be confused with proof of their <Hamiltonian> involution.
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