  Perturbations of a class of semiclassical spiky strings in three dimensional
Anti-de Sitter (AdS) spacetime, are investigated using the well-known Jacobi
equations for small, normal deformations of an embedded timelike surface. We
show that the equation for the perturbation scalar which governs the behaviour
of such small deformations, is a special case of the well-known
Darboux-Treibich-Verdier (DTV) equation. The eigenvalues and eigensolutions of
the DTV equation for our case are obtained by solving certain continued
fractions numerically. These solutions are thereafter utilised to further
demonstrate that there do exist finite perturbations of the AdS spiky strings.
Our results therefore establish that the spiky string configurations in AdS3
are indeed stable against small fluctuations. Comments on future possibilities
of work are included in conclusion.
