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Higher-order rogue wave-like solutions for a nonautonomous nonlinear Schrödinger equation with external potentials

Author

Listed:
  • Liu, Lei
  • Tian, Bo
  • Wu, Xiao-Yu
  • Sun, Yan

Abstract

Under investigation in this paper is the higher-order rogue wave-like solutions for a nonautonomous nonlinear Schrödinger equation with external potentials which can be applied in the nonlinear optics, hydrodynamics, plasma physics and Bose–Einstein condensation. Based on the Kadomtsev–Petviashvili hierarchy reduction, we construct the Nth order rogue wave-like solutions in terms of the Gramian under the integrable constraint. With the help of the analytic and graphic analysis, we exhibit the first-, second- and third-order rogue wave-like solutions through the different dispersion, nonlinearity and linear potential coefficients. We find that only if the dispersion and nonlinearity coefficients are proportional to each other, heights of the background of those rogue waves maintain unchanged with time increasing. Due to the existence of complex parameters, such nonautonomous rogue waves in the higher-order cases have more complex features than those in the lower.

Suggested Citation

  • Liu, Lei & Tian, Bo & Wu, Xiao-Yu & Sun, Yan, 2018. "Higher-order rogue wave-like solutions for a nonautonomous nonlinear Schrödinger equation with external potentials," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 492(C), pages 524-533.
    • Handle: RePEc:eee:phsmap:v:492:y:2018:i:c:p:524-533
    DOI: 10.1016/j.physa.2017.09.024
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    Cited by:

    1. Li, Liu-Qing & Gao, Yi-Tian & Yu, Xin & Ding, Cui-Cui & Wang, Dong, 2022. "Bilinear form and nonlinear waves of a (1+1)-dimensional generalized Boussinesq equation for the gravity waves over water surface," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 198(C), pages 494-508.

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