We present a novel one-dimensional nonlinear evolution equation governing the dynamics short-wavelength longitudinal waves in a nonrelativistic fully degenerate quantum plasma using kinetic equation for the Wigner function. The linear dispersion of the equation has a form of “zero sound” , where k is the wave number, and it strongly differs from previously known nonlinear evolution equations. We numerically find the corresponding soliton solutions and demonstrate that the collisions between three solitons turn out to be elastic, resulting only in phase shifts.
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