Stability of Gaussian-type soliton in the cubic–quintic nonlinear media with fourth-order diffraction and \[\mathcal {PT}\] -symmetric potentials

• Published in: Nonlinear dynamics Vol. 98; no. 1; pp. 317 - 326
• Main Authors: Camus Gaston Latchio Tiofack, Tchepemen, Nathan Nkouessi, Alidou Mohamadou, Kofané, Timoléon Crépin
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Nature B.V 01-10-2019
• Subjects: Anharmonicity; Coefficients; Computer simulation; Diffraction; Nonlinearity; Power flow; Solitary waves; Stability analysis
• ISSN: 0924-090X; 1573-269X
• DOI: 10.1007/s11071-019-05193-1

We report on the existence and stability of Gaussian-type soliton in the nonlinear Schrödinger (NLS) equation with interplay of cubic–quintic nonlinearity, fourth-order diffraction (FOD) and novel quartic anharmonic parity-time (\[\mathcal {PT}\])-symmetric Gaussian potential. We study numerically the impact of the FOD coefficient on the regions of unbroken/broken linear \[\mathcal {PT}\]-symmetric phases. In the nonlinear domain, we derive exact soliton solutions of the one-dimensional and two-dimensional cubic–quintic NLS equation with \[\mathcal {PT}\]-symmetric Gaussian potential and FOD coefficients. Moreover, the stability of the constructed soliton solution is investigated. The results of linear stability analysis are validated by comparison with numerical simulations. Furthermore, we also show that the relative strength of the FOD coefficient influences the direction of the power flow.