Reply to Comment on: ''Exact solutions of the Lawrence-Doniach model for   layered superconductors''
  In the recent Comment [V. M. Krasnov, Phys. Rev. B vol. 65, 096503 (2002)], the author claims to have ''disproved'' our theoretical conclusion [S. V. Kuplevakhsky, Phys. Rev. B vol. 60, 7496 (1999); Phys. Rev. B vol. 63, 054508 (2001)] that isolated Josephson vortices in layered superconductors and stacked junctions are absolutely unstable in the presence of an external field. We show that this claim has no grounds. Moreover, by solving an appropriate boundary value problem, we obtain a complete classification of soliton (vortex) solutions to coupled static sine-Gordon equations. We also discuss the problem of vortex penetration and analyze available experimental data. 
Sergey V. Kuplevakhsky (Kharkov National University, Kharkov, Ukraine)