Abstract
The problem of Liouvillian integrability for the classical force-free generalized Duffing oscillators is solved completely. All the cases when the generalized Duffing oscillators possess Liouvillian first integrals are classified. It is shown that the general solutions in integrable cases are expressible via elliptic and hyperelliptic functions. The relationship between the generalized Duffing systems and the Newell–Whitehead–Segel equation is used to characterize algebraically invariant traveling waves of the latter.
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