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

Pair-production of cusps on a string in AdS$_3$