  The classical motion of a Nambu-Goto string in AdS$_3$ spacetime is governed
by the generalized sinh-Gordon equation. It can locally be reduced to the
sinh-Gordon (shG), cosh-Gordon (chG), or Liouville equation, depending on the
value of the scalar curvature of the induced metric. In this paper, I examine
solutions that contain both shG-type and chG-type regions. The boundary between
these regions moves with the speed of light. I show that near such boundaries
(generalized) solitons can be classically pair-produced. The solitons move
subluminally (superluminally) in the shG (chG) region on the worldsheet, and
they correspond to cusps on the string. A direct energy cascade is observed at
the moment of pair-creation.
  For the calculations, I use an exact discretization of the equation of
motion. The solutions are segmented strings. In this discrete system,
pair-production leads to a complete evaporation of the shG region. The final
state is a gas of cusps in a chG environment. A Mathematica notebook that has
been used to generate the relevant figures is attached.
