caa a22 4500 475805313 CHVBK 20180406123745.0 cr unu---uuuuu 170329e20000601xx s 000 0 eng 10.1007/s003329910012 doi (NATIONALLICENCE)springer-10.1007/s003329910012 Nonfocusing Instabilities in Coupled, Integrable Nonlinear Schrödinger pdes [Elektronische Daten] [M. G. Forest, D. W. McLaughlin, D. J. Muraki, O. C. Wright] 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]. Springer-Verlag New York Inc., 2000 Key words. Defocusing instabilities, homoclinic orbits, coupling instabilities, integrable pdes, birefringent fibers nationallicence Forest M. G. Department of Mathematics, The University of North Carolina at Chapel Hill, Chapel Hill, NC 27599-3250, USA, US aut McLaughlin D. W. Courant Institute of Mathematical Sciences, New York, NY 10012, USA, US aut Muraki D. J. Courant Institute of Mathematical Sciences, New York, NY 10012, USA, US aut Wright O. C. Department of Mathematics, The University of North Carolina at Chapel Hill, Chapel Hill, NC 27599-3250, USA, US aut Journal of Nonlinear Science Springer-Verlag 10/3(2000-06-01), 291-331 0938-8974 10:3<291 2000 10 332 https://doi.org/10.1007/s003329910012 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s003329910012 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Forest M. G. Department of Mathematics, The University of North Carolina at Chapel Hill, Chapel Hill, NC 27599-3250, USA, US aut NATIONALLICENCE 700 1- McLaughlin D. W. Courant Institute of Mathematical Sciences, New York, NY 10012, USA, US aut NATIONALLICENCE 700 1- Muraki D. J. Courant Institute of Mathematical Sciences, New York, NY 10012, USA, US aut NATIONALLICENCE 700 1- Wright O. C. Department of Mathematics, The University of North Carolina at Chapel Hill, Chapel Hill, NC 27599-3250, USA, US aut NATIONALLICENCE 773 0- Journal of Nonlinear Science Springer-Verlag 10/3(2000-06-01), 291-331 0938-8974 10:3<291 2000 10 332 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer