A solid-core photonic-crystal fiber (PCF) with an effective mode area of 20 microm2 is used to demonstrate the generation of sub-100-kW, 30-70 fs wavelength-tunable solitons within a wavelength range of 1300-1800 nm at a repetition rate of 18 MHz. An energy of 2.9 nJ per pulse is achieved for a 35 fs soliton PCF output centered at 1770 nm. Our numerical analysis supports experimental findings and suggests that frequency-shifted solitons in solid-core PCFs can be scaled up to a submegawatt level of peak powers.