We present an approach for instabilities of solitons that is based on the spectrum of a fourth-order linearized operator. Unlike the standard approach which is based on the slope (Vakhitov–Kolokolov) condition, this approach provides the quantitative value of the instability rate and the qualitative nature of the instability dynamics.
© 2011 Optical Society of America
Original Manuscript: October 29, 2010
Revised Manuscript: December 21, 2010
Manuscript Accepted: December 22, 2010
Published: January 31, 2011
Boaz Ilan, Yonatan Sivan, and Gadi Fibich, "A quantitative approach to soliton instability," Opt. Lett. 36, 397-399 (2011)