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Research in ultrasonography has evidenced the propagation of a peculiar kind of excitation in fluids. Such excitation, dubbed a X-wave, has characteristics resembling that of a solitary-wave type. We reconsider the problem in a medium consisting of a biological material of the like of alpha-helix proteins. It can be shown that in this case is expected an excitation of the Davydov's solitary wave type, however strongly damped in normal conditions. The case of acetanilide, an organic polymer which resembles biopolymers, is considered, and the infrared spectrum analyzed. Davydov's soliton is evidenced as a coherent state of polar vibrations. The case of acoustic (sound) vibrations is also considered, where, also, a damped Davydov-like solitary wave may be excited. However, it is shown that when traveling in conditions sufficiently away from equilibrium, more precisely, when the soliton is embeded in the resulting Frohlich-Bose-Einstein condensate, the lifetime of the solitary wave is largely enhanced. Moreover, a soliton moving in bulk with a velocity larger than that of the group velocity of the normal vibrational waves would produce a Cherenkov-like emission of phonons giving rise to the observed X-wave-like pattern. This paper is a modified and extended version of an earlier publication on the subject

Considerations on undistorted-progressive X-waves and Davydov solitons, Fröhlich-Bose-Einstein condensation, and Cherenkov-like effect in biosystems