Abstract
This paper shows that a special class of smooth nonlinear oscillators, called bisuperlinear, urn:x-wiley:00222526:media:sapm199696185:sapm199696185-math-0001 has a family of adiabatically symmetric solutions. This was motivated by a problem studied in sloshing water waves. A potential application of the work is to compute the nontrivial leading order term of the adiabatic invariants for a certain type of nonlinear nearly periodic Hamiltonian systems.
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