Optical Solitons of the Nonlinear Schrödinger Equation Without Self-Phase Modulation: Two Different Techniques

İlker Burak Giresunlu; Bengi Yıldız

doi:10.33401/fujma.1588546

Optical Solitons of the Nonlinear Schrödinger Equation Without Self-Phase Modulation: Two Different Techniques

Abstract

In this paper, the nonlinear Schrödinger equation (NLSE) without self-phase modulation (SPM) is investigated. The new Kudryashov method and the auxiliary equation method are employed to derive various classes of exact analytical solutions. The obtained solutions include bright and dark soliton structures, periodic waves, rational singular solutions, and plane-wave profiles, depending on the parameter choices. The bright-soliton solution obtained through the Kudryashov method recovers, under a reduced-dispersion limit, a previously reported solution in Ref. [6]. The hyperbolic bright/dark solution families obtained by the auxiliary equation method partially reproduce known results while extending the corresponding solution structures, whereas, to the best of our knowledge, the periodic and rational singular solution families have not been previously reported for the considered higher-order NLSE. Representative graphical illustrations are provided to demonstrate the qualitative behavior of the obtained wave structures, and the physical characteristics and admissibility of the localized solutions are discussed.

Keywords

Supporting Institution

This research received no external funding.

Ethical Statement

This article does not contain any studies with human or animal subjects. It is declared that during the preparation process of this study, scientific and ethical principles were followed and all the studies benefited from are stated in the bibliography.

Thanks

The author would like to express their sincere thanks to the editor and the anonymous reviewers for their helpful comments and suggestions.

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Details

Primary Language

English

Subjects

Applied Mathematics (Other)

Journal Section

Research Article

Authors

İlker Burak Giresunlu ^*
0000-0002-2190-0003
Türkiye

Bengi Yıldız
0000-0002-3980-3578
Türkiye

Publication Date

September 30, 2026

Submission Date

November 20, 2024

Acceptance Date

September 28, 2026

Published in Issue

Year 2026 Volume: 9 Number: 3

DOI

https://doi.org/10.33401/fujma.1588546

IZ

https://izlik.org/JA45LU35MW

Cite

RIS / Bibtex

APA

Giresunlu, İ. B., & Yıldız, B. (2026). Optical Solitons of the Nonlinear Schrödinger Equation Without Self-Phase Modulation: Two Different Techniques. Fundamental Journal of Mathematics and Applications, 9(3), 163-178. https://doi.org/10.33401/fujma.1588546

AMA

1.Giresunlu İB, Yıldız B. Optical Solitons of the Nonlinear Schrödinger Equation Without Self-Phase Modulation: Two Different Techniques. Fundam. J. Math. Appl. 2026;9(3):163-178. doi:10.33401/fujma.1588546

Chicago

Giresunlu, İlker Burak, and Bengi Yıldız. 2026. “Optical Solitons of the Nonlinear Schrödinger Equation Without Self-Phase Modulation: Two Different Techniques”. Fundamental Journal of Mathematics and Applications 9 (3): 163-78. https://doi.org/10.33401/fujma.1588546.

EndNote

Giresunlu İB, Yıldız B (September 1, 2026) Optical Solitons of the Nonlinear Schrödinger Equation Without Self-Phase Modulation: Two Different Techniques. Fundamental Journal of Mathematics and Applications 9 3 163–178.

IEEE

[1]İ. B. Giresunlu and B. Yıldız, “Optical Solitons of the Nonlinear Schrödinger Equation Without Self-Phase Modulation: Two Different Techniques”, Fundam. J. Math. Appl., vol. 9, no. 3, pp. 163–178, Sept. 2026, doi: 10.33401/fujma.1588546.

ISNAD

Giresunlu, İlker Burak - Yıldız, Bengi. “Optical Solitons of the Nonlinear Schrödinger Equation Without Self-Phase Modulation: Two Different Techniques”. Fundamental Journal of Mathematics and Applications 9/3 (September 1, 2026): 163-178. https://doi.org/10.33401/fujma.1588546.

JAMA

1.Giresunlu İB, Yıldız B. Optical Solitons of the Nonlinear Schrödinger Equation Without Self-Phase Modulation: Two Different Techniques. Fundam. J. Math. Appl. 2026;9:163–178.

MLA

Giresunlu, İlker Burak, and Bengi Yıldız. “Optical Solitons of the Nonlinear Schrödinger Equation Without Self-Phase Modulation: Two Different Techniques”. Fundamental Journal of Mathematics and Applications, vol. 9, no. 3, Sept. 2026, pp. 163-78, doi:10.33401/fujma.1588546.

Vancouver

1.İlker Burak Giresunlu, Bengi Yıldız. Optical Solitons of the Nonlinear Schrödinger Equation Without Self-Phase Modulation: Two Different Techniques. Fundam. J. Math. Appl. 2026 Sep. 1;9(3):163-78. doi:10.33401/fujma.1588546