We know that the modified Korteweg-de Vries (mKdV), the sine-Gordon (sG), and the mKdV-sG models can describe few-cycle optical pulse propagation beyond the slowly-varying-envelope approximation in transparent media. We show numerically that these models are also able to describe the generation of supercontinua with spectral bandwidths of several octaves. Several mechanisms of spectral broadening are highlighted, involving self-phase modulation, parametric interactions of high harmonics, and few-cycle-soliton generation.