Two Approaches for Investigation of Soliton Pulse in a Nonlinear Medium

  • I. A. Molotkov
  • N. I. Manaenkova
Part of the NATO Science Series book series (NAII, volume 31)


In this paper, we discuss the use of a generalized nonlinear Schrödinger equation
$$ i\psi _x + \psi _{tt} + 2|\psi |^2 \psi - i\beta \psi _{ttt} + i\gamma \left( {|\psi |^2 \psi } \right), = 0, \beta > 0, \gamma > 0 $$
for the complex amplitude ψ(x,t) of the light guide pulse envelope. The use of the subpicosecond and femtosecond pulses gives one many additional opportunities for light guides devices and, in particular, opportunity to increase transmitted powers. However in the mentioned ranges it is necessary more accurate to take into account nonlinear and dispersion effects. There are serious theoretical arguments [1, 2, 3], that the additional terms with β and γ in (1) permit one to describe transition to the sub- picosecond range. It is necessary to note, that these terms naturally appear under consecutive asymptotic derivation of the equation of type (1) in [4]. The highest nonlinear term was taken into account in [1, 5, 6, 7], and term Ψ m is considered by [6, 7, 8].


Cauchy Problem Additional Term Light Guide Nonlinear Schrodinger Equation Soliton Pulse 
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Copyright information

© Springer Science+Business Media Dordrecht 2001

Authors and Affiliations

  • I. A. Molotkov
    • 1
  • N. I. Manaenkova
    • 1
  1. 1.Institute of Terrestrial Magnetizm, Ionosphere and Radio Wave Propagation Russian Academy of ScienceMoscow RegionRussia

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