Simulation of a class E power oscillator using LTspice
I see the inductors are showing the dot, that's usually if there is some coupling (unless manually shown). Here's my attempt, no coupling:



and some details for the waveforms as in your example. Note that V(x) is V(RL+), and I used parasitics for the supply, which means the current through it incorporates what would have been your capacitors (if you had some resistance between the supply and the caps, as per the comment):