Journal of Nonlinear Science

, Volume 10, Issue 3, pp 291–331

Nonfocusing Instabilities in Coupled, Integrable Nonlinear Schrödinger pdes

  • M. G. Forest
  • D. W. McLaughlin
  • D. J. Muraki
  • O. C. Wright
Article

DOI: 10.1007/s003329910012

Cite this article as:
Forest, M., McLaughlin, D., Muraki, D. et al. J. Nonlinear Sci. (2000) 10: 291. doi:10.1007/s003329910012

nonfocusing

instabilities that exist independently of the well-known modulational instability of the focusing NLS equation. The focusing versus defocusing behavior of scalar NLS fields is a well-known model for the corresponding behavior of pulse transmission in optical fibers in the anomalous (focusing) versus normal (defocusing) dispersion regime [19], [20]. For fibers with birefringence (induced by an asymmetry in the cross section), the scalar NLS fields for two orthogonal polarization modes couple nonlinearly [26]. Experiments by Rothenberg [32], [33] have demonstrated a new type of modulational instability in a birefringent normal dispersion fiber, and he proposes this cross-phase coupling instability as a mechanism for the generation of ultrafast, terahertz optical oscillations. In this paper the nonfocusing plane wave instability in an integrable coupled nonlinear Schrödinger (CNLS) partial differential equation system is contrasted with the focusing instability from two perspectives: traditional linearized stability analysis and integrable methods based on periodic inverse spectral theory. The latter approach is a crucial first step toward a nonlinear , nonlocal understanding of this new optical instability analogous to that developed for the focusing modulational instability of the sine-Gordon equations by Ercolani, Forest, and McLaughlin [13], [14], [15], [17] and the scalar NLS equation by Tracy, Chen, and Lee [36], [37], Forest and Lee [18], and McLaughlin, Li, and Overman [23], [24].

Key words. Defocusing instabilities, homoclinic orbits, coupling instabilities, integrable pdes, birefringent fibers

Copyright information

© Springer-Verlag New York Inc. 2000

Authors and Affiliations

  • M. G. Forest
    • 1
  • D. W. McLaughlin
    • 2
  • D. J. Muraki
    • 2
  • O. C. Wright
    • 1
  1. 1.Department of Mathematics, The University of North Carolina at Chapel Hill, Chapel Hill, NC 27599-3250, USAUS
  2. 2.Courant Institute of Mathematical Sciences, New York, NY 10012, USAUS