Nonlinear pulse compression technology permits practitioners to produce ultrashort pulses for integrated frequency comb generation and optical coherence tomography. However, onchip simultaneous combination and compression of two pulses at 2.0 µm is a complex nonlinear dynamic that has never been reported. Here, we demonstrate that two raised cosine pulses with the same center wavelengths of 2.0 µm are firstly coalesced into a single combined pulse and then realize nearly self-similar compression in the dispersion exponentially decreasing silicon waveguide, where the final compressed pulse was reduced from 200 fs to 49 fs with a compression factor of 4.08. Additionally, the peak power of the compressed pulse steadily rises to 2.16 times of the initial peak power. For further development, we also illustrate two input pulses with different center wavelengths to realize effective combination and self-similar compression. These results shed new insights into the potential of dispersion engineering waveguides for low-power integrated applications at 2.0 µm.