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Abstract

A detailed mathematical analysis is undertaken of solitary wave solutions of a system of coupled NLS equations describing second harmonic generation in optical materials with chi^2 solutions of a system of coupled NLS equations describing second harmonic generation in optical materials with chi^2 nonlinearity. The so called bright-bright case is studied exclusively. The system depends on a single dimensionless parameter alpha which includes both wave and material properties. Using variational methods, the first rigorous mathematical proof is given that at least one solitary wave exists for all positive alpha. Recently bound states (multi-pulsed solitary waves) have been found numerically. Using numerical continuation, the region of existence of these solutions is revealed to be alpha in (0,1) and the bifurcations occuring at the two extremes of this interval are uncovered.
Original languageEnglish
Publication statusUnpublished - 1997

Bibliographical note

Additional information: Preprint of a paper later published by Springer (1999), Journal of Nonlinear Science, 9(1), pp.33-52, ISSN 0938-8974

Keywords

  • coupled NLS equations
  • variational methods
  • nonlinearity
  • solitary wave solutions
  • bright-bright case
  • numerical continuation

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