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Vector rational and semi-rational rogue waves for the coupled cubic-quintic nonlinear Schrödinger system in a non-Kerr medium. (English) Zbl 1437.35622
Summary: Non-Kerr media possess certain applications in photonic lattices and optical fibers. Studied in this paper are the vector rational and semi-rational rogue waves in a non-Kerr medium, through the coupled cubic-quintic nonlinear Schrödinger system, which describes the effects of quintic nonlinearity on the ultrashort optical pulse propagation in the medium. Applying the gauge transformations, we derive the \(N\) th-order Darboux transformation and \(N\) th-order vector rational and semi-rational rogue wave solutions, where \(N\) is a positive integer. With such solutions, we present three types of the second-order rogue waves with the triangle structure: the one with each component containing three four-petaled rogue waves, the one with each component containing three eye-shaped rogue waves, and the other with one component containing three anti-eye-shaped rogue waves and the other component containing three eye-shaped rogue waves. We exhibit the third-order vector rogue waves with the merged, triangle and pentagon structures in each component. Moreover, we show the first- and second-order vector semi-rational rogue waves which display the coexistence of the rogue waves and the breathers.

MSC:
35Q55 NLS equations (nonlinear Schrödinger equations)
35Q51 Soliton equations
78A60 Lasers, masers, optical bistability, nonlinear optics
37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems
37K35 Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems
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