Work

Quiescent optical solitons with nonlinear Schrödinger’s equation having Kerr law of self-phase modulation and intensity-dependent dispersion

Year: 2026

Type: article

Abstract: Quiescent optical solitons provide stationary localized states in media where nonlinear dispersion can suppress ordinary wave translation. Motivated by the need to understand this mechanism, we study a Kerr-type nonlinear Schrödinger equation containing two intensity-dependent dispersive corrections. The objective is to determine the admissible real-profile wave reduction and construct its exact stationary solutions. A Lie-symmetry analysis shows that, when the envelope-curvature correction is active, a nonconstant localized real profile cannot sustain a nonzero carrier wavenumber or propagation velocity; consequently, the admissible localized structures are quiescent. The resulting nonlinear ordinary differential equation is solved using the enhanced direct algebraic method. Under the closure condition associated with the adopted auxiliary-function ansatz, bright, dark kink-type, singular, Jacobi elliptic, Weierstrass elliptic, and straddled solution families are derived. Their limiting connections are established, demonstrating how elliptic and straddled profiles recover standard hyperbolic solitons.

Source: Ain Shams Engineering Journal

DOI: 10.1016/j.asej.2026.104408

Authors: Ahmed H. Arnous, Muhammad Amin S. Murad, Luminita Moraru, Yakup Yildirim, Anjan Biswas

Institutions: Jadara University, Saveetha University, University of Duhok, Karadeniz Technical University, Sefako Makgatho Health Sciences University, "Dunarea de Jos" University of Galati, Biruni University, Near East University, Khazar University, Grambling State University

Language: English

Topic: Nonlinear Waves and Solitons

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,200

OpenAlex ID: W7203890241

FWCI: 3.516

Cites: 27

Cited by: 1

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