The pressure dependence of the nonlinearity coefficient a of the roton seco
nd sound in superfluid He-II at pressures up to 25 bar has been studied. It
has been found that with increasing pressure the temperature T-alpha, at w
hich the coefficient a goes through zero, is lowered from 1.88 to 1.58 K. I
t means that at all pressures up to the freezing of the superfluid liquid t
here exists a wide range of temperatures T-alpha < T < T-lambda where the n
onlinearity coefficient is negative: alpha < 0. In propagating compressiona
l wave of second sound, it corresponds to a positive oscillation of the tem
perature in He-II, and a temperature discontinuity (shock) should appear at
the back side of the pulse. On generating a bipolar second sound pulse wit
h shock in its middle, the width of the pulse does not change with distance
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