  This paper is devoted to the study of the existence and uniqueness of global
admissible conservative weak solutions for the periodic single-cycle pulse
equation. We first transform the equation into an equivalent semilinear system
by introducing a new set of variables. Using the standard ordinary differential
equation theory, we then obtain the global solution to the semilinear system.
Next, returning to the original coordinates, we get the global admissible
conservative weak solution for the periodic single-cycle pulse equation.
Finally, given an admissible conservative weak solution, we find a equation to
single out a unique characteristic curve through each initial point and prove
the uniqueness of global admissible conservative weak solution without any
additional assumptions.
