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The Generalized Pochammer-Chree Equations govern the propagation of longitudinal waves in elastic rods.
Limited analytic results exist for the occurrence of one family of solitary wave solutions of these equations.
Since solitary wave solutions often play a central role in the long-time evolution of an initial disturbance, we consider
such solutions here (via normal form approach) within the framework of reversible systems theory. Besides confirming
the existence of the known family of solitary waves, we find a continuum of delocalized solitary waves
(or homoclinics to small-amplitude periodic orbits).
On isolated curves in the relevant parameter region, the delocalized waves reduce to genuine embedded solitons.
The new family of solutions occur in regions of parameter space distinct from the known solitary wave solutions and
are thus entirely new. Directions for future work are also mentioned.