TY - JOUR

T1 - Self-similar parabolic optical solitary waves

AU - Boscolo, Sonia

AU - Turitsyn, Sergei K.

AU - Novokshenov, V.Yu.

AU - Nijhof, J.H.B.

PY - 2002/12

Y1 - 2002/12

N2 - We study solutions of the nonlinear Schrödinger equation (NLSE) with gain, describing optical pulse propagation in an amplifying medium. We construct a semiclassical self-similar solution with a parabolic temporal variation that corresponds to the energy-containing core of the asymptotically propagating pulse in the amplifying medium. We match the self-similar core through Painlevé functions to the solution of the linearized equation that corresponds to the low-amplitude tails of the pulse. The analytic solution accurately reproduces the numerically calculated solution of the NLSE.

AB - We study solutions of the nonlinear Schrödinger equation (NLSE) with gain, describing optical pulse propagation in an amplifying medium. We construct a semiclassical self-similar solution with a parabolic temporal variation that corresponds to the energy-containing core of the asymptotically propagating pulse in the amplifying medium. We match the self-similar core through Painlevé functions to the solution of the linearized equation that corresponds to the low-amplitude tails of the pulse. The analytic solution accurately reproduces the numerically calculated solution of the NLSE.

KW - generation of parabolic pulses

KW - nonlinear optics

KW - self-similarity

UR - http://www.scopus.com/inward/record.url?scp=0036451108&partnerID=8YFLogxK

UR - http://www.springerlink.com/content/p84p80qq6j787w16/

U2 - 10.1023/A:1021402024334

DO - 10.1023/A:1021402024334

M3 - Article

VL - 133

SP - 1647

EP - 1656

JO - Theoretical and Mathematical Physics

JF - Theoretical and Mathematical Physics

SN - 0040-5779

IS - 3

ER -