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  • Articles: DFG German National Licenses  (2)
  • Brusselator  (1)
  • Key words. Solitons, nonlinear optical pulse propagation, optical fibers, stability.  (1)
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  • Articles: DFG German National Licenses  (2)
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Years
Keywords
  • 1
    Electronic Resource
    Electronic Resource
    Spontaneous oscillations in two 2-component cells coupled by diffusion (1986)
    Springer
    Journal of mathematical biology 23 (1986), S. 205-219 
    Details
    ISSN: 1432-1416
    Keywords: Coupled oscillators ; Diffuse instabilities ; Brusselator ; Glycolytic oscillations ; Hopf bifurcation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Mathematical examples are presented of oscillators with two variables which do not oscillate in isolation, but which do oscillate stably when coupled with a twin via difiusion. Two examples are presented, the LefeverPrigogine Brusselator and a system used to model glycolytic oscillations. The mathematical method is not the usual bifurcation theory, but rather a type of singular perturbation theory combined with bifurcation theory. For both examples, it is shown that all stationary solutions are unstable for appropriate parameter settings. In the case of the Brusselator, it is further shown that there exist limit cycles; i.e. stable oscillations, in this parameter range. A numerical example is presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00276957
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Stability of pulses on optical fibers with phase-sensitive amplifiers (1997)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 48 (1997), S. 175-192 
    Details
    ISSN: 0044-2275
    Keywords: Key words. Solitons, nonlinear optical pulse propagation, optical fibers, stability.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract. Pulse stability is crucial to the effective propagation of information in a soliton-based optical communication system. It is shown in this paper that pulses in optical fibers, for which attenuation is compensated by phase-sensitive amplifiers, are stable over a large range of parameter values. A fourth-order nonlinear diffusion model due to Kutz and co-workers is used. The stability proof invokes a number of mathematical techniques, including the Evans function and Grillakis' functional analytic approach.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/PL00001473
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    Paper (German National Licenses)
    Fulltext
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