Breathers, solitons and rogue waves of the quintic nonlinear Schrödinger equation on various backgrounds Academic Article uri icon

abstract

  • © 2019, Springer Nature B.V. We investigate the generation of breathers, solitons, and rogue waves of the quintic nonlinear Schrödinger equation (QNLSE) on uniform and elliptical backgrounds. The QNLSE is the general nonlinear Schrödinger equation that includes all terms up to the fifth-order dispersion. We use Darboux transformation to construct initial conditions for the dynamical generation of localized high-intensity optical waves. The condition for the breather-to-soliton conversion is provided with the analysis of soliton intensity profiles. We discover a new class of higher-order solutions in which Jacobi elliptic functions are set as background seed solutions of the QNLSE. We also introduce a method for generating a new class of rogue waves—the periodic rogue waves—based on the matching of the periodicity of higher-order breathers with the periodicity of the background dnoidal wave.

author list (cited authors)

  • Nikolić, S. N., Ashour, O. A., Aleksić, N. B., Belić, M. R., & Chin, S. A.

citation count

  • 6

publication date

  • January 2019