https://doi.org/10.1007/s100530050098
A variational approach of nonlinear dissipative pulse propagation
1
Grupo de Fotonica, I.N.A.O.E.,
Apartado Postal 51 y 216, 72000
Puebla, Mexico
2
Departamento de Física,
Universidade Federal de Alagoas,
Maceió AL 57072-970, Brazil
Corresponding author: a solange@lux.ufal.br
Received:
4
August
1997
Revised:
25
November
1997
Accepted:
14
January
1998
Published online: 15 March 1998
A variational technique to deal with nonlinear dissipative pulse propagation is established. By means of a generalization of the Kantorovitch method, suitable for non-conservative systems, we are able to cope with an extended nonlinear Schrödinger equation (NLSE) which describes pulse propagation under the influence of nonlinear loss and/or gain, in particular, in the presence of two-photon absorption (TPA). Based on the characteristics of the exact solution of the NLSE in the absence of TPA, we investigate the effects of frequency dispersion of the nonlinear susceptibility associated to the two-photon resonance, obtaining the necessary conditions for a solitary wave solution, even in the presence of a self-steepening term.
PACS: 42.65.-k – Nonlinear optics / 03.40.Kf – Waves and wave propagation: general mathematical aspects / 52.35.Mw – Nonlinear waves and nonlinear wave propagation (including parametric effects, mode coupling, ponderomotive effects, etc.)
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 1998
