Regular Article

Stable solitons in the one- and two-dimensional generalized cubic-quintic nonlinear Schrödinger equation with fourth-order diffraction and 𝒫𝒯-symmetric potentials

¹ Pure Physics Laboratory, Group of Nonlinear Physics and Complex Systems, Department of Physics, Faculty of Science, University of Douala, P.O. Box 24157, Douala, Cameroon
² Laboratory of Mechanics, Department of Physics, Faculty of Science, University of Yaounde I, P.O. Box 812, Yaounde, Cameroon
³ Centre d’Excellence Africain des Technologies de l’Information et de la Communication (CETIC), University of Yaounde I, Yaounde, Cameroon
⁴ Condensed Matter Laboratory, Department of Physics, Faculty of Science, University of Maroua, P.O. Box 814, Maroua, Cameroon
⁵ The Abdus Salam International Centre for Theoretical Physics, P.O. Box 538, Strada Costiera 11, I-34014 Trieste, Italy

^a e-mail: tchepemen@live.fr

Received: 31 August 2019
Received in final form: 3 January 2020
Published online: 19 February 2020

Abstract

Both one-dimensional and two-dimensional localized mode families in parity-time (𝒫𝒯)-symmetric potentials with competing cubic-quintic nonlinearities and higher-order diffraction are reported. In particular, we investigate the role played by the competing nonlinearities and fourth-order diffraction parameter on the beam dynamics in the generalized 𝒫𝒯-symmetric Scarf potentials. The numerical fundamental soliton in competing nonlinearities (1-D double peaked solitons) can be found to be stable around the propagation parameter for exact soliton. A linear stability analysis corroborated by direct numerical simulation reveals that the regions of stability of these solutions can be controlled by tuning the values of the FOD parameters as well as by tuning the sign of the cubic and quintic nonlinearities. In particular, we have shown that the FOD parameter can be used to provide the restoration of the stability of the solitons.