One of the most interesting extensions of the DNLS equation is in the study of multicomponent versions of the model. Such models are relevant both in nonlinear optics, e.g., when propagating multiple frequencies or polarizations of light; prototypical examples of these types have been discussed, e.g., in [1, 2] from the theoretical point of view and in [3] from the experimental point of view (see also references therein). On the other hand, similar models are quite relevant to two-component [4] or even one-component BECs [5] in the presence of optical lattice potentials. The coupling between the different components can be linear or nonlinear (or both) [1]. In this chapter, we show some case examples of interesting dynamics that can arise in the linear coupling case (symmetry breaking), as well as ones that can arise in the nonlinear coupling case (dynamical instabilities).
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Keywords
- Bifurcation Diagram
- Transverse Magnetic
- Transverse Electric
- Elliptically Polarize
- Numerical Continuation
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Kevrekidis, P.G. (2009). MultiComponent DNLS Equations. In: The Discrete Nonlinear Schrödinger Equation. Springer Tracts in Modern Physics, vol 232. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89199-4_7
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