| Abstract: |
| The approximate partial Hamiltonian systems for the
characterization of associated approximate operators and first
integrals are investigated. It is proved that if an approximate operator
is an approximate partial Hamiltonian operator which provides a
first integral, then its evolutionary representative is an approximate partial Hamiltonian
operator providing a first integral. The extra
operator conditions are provided for an approximate partial Hamiltonian
operator in evolutionary form to yield an approximate first
integral. Moreover, characterization of approximate partial
Hamiltonian operators and associated first integral conditions are
explicitly provided for the approximate Hamiltonian system.
Several examples are constructed to explain the theory. |
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