We calculate the power spectrum of the stochastic gravitational wave (GW) background expected from kink-kink collisions on infinite cosmic strings. Intersections in the cosmic string network continuously generate kinks, which emit GW bursts by their propagation on curved strings as well as by their collisions. First, we show that the GW background from kink-kink collisions is much larger than the one from propagating kinks at high frequencies because of the higher event rate. We then propose a method to take into account the energy loss of the string network by GW emission as well as the decrease of kink number due to the GW backreaction. We find that, even though these effects reduce the amplitude of the GW background, we can obtain a constraint on the string tension $Gmulesssim 2 times 10^{-7}$ using the current upper bound on the GW background by Advanced-LIGO, which is as competitive as the constraint from cusps on string loops.
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