A hybrid mechanism of ion acceleration is investigated which demonstrates the higher spectral density of protons at high energies. The interaction of few-cycle terrawatt laser pulses with near-critical density gas target is studied with the help of two-dimensional particle-in-cell simulation. The generation of few MeV protons with high spectral concentration near cutoff is attributed to the propagation of solitary waves in the decaying density profile of the gas jet. Plasma dynamics at longer time scale is explained by semianalytical modeling and conditions for solitary wave breaking are presented.