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Rogue wave solutions for the coupled cubic-quintic nonlinear Schrödinger equations with variable coefficients. (English) Zbl 1335.78004

Summary: In this paper, by the Darboux transformation, we get the vector rogue wave solutions of the coupled cubic-quintic nonlinear Schrödinger equations with variable coefficients, which come from twin-core nonlinear optical fibers and waveguides, describing the effects of quintic nonlinearity on the ultrashort optical pulse propagation in the non-Kerr media. The first-order vector rogue wave solutions obtained in this paper can admit certain different patterns. Dynamical features of the rogue wave solutions are graphically investigated. These results might be of some value for the ultrashort optical pulse propagation in the non-Kerr media.

MSC:

78A50 Antennas, waveguides in optics and electromagnetic theory
78A60 Lasers, masers, optical bistability, nonlinear optics
35Q55 NLS equations (nonlinear Schrödinger equations)
68W30 Symbolic computation and algebraic computation
37K35 Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems
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