Optical Soliton Solutions of a $(3+1)$-Dimensional Nonlinear Schrödinger Equation with Cubic-Quintic-Septic Nonlinearity

Mehmet Fatih Uçar

doi:10.36753/mathenot.1670727

EN

Optical Soliton Solutions of a $(3+1)$-Dimensional Nonlinear Schrödinger Equation with Cubic-Quintic-Septic Nonlinearity

Abstract

In this paper, we studied the extended (3+1)-dimensional NLSE that has cubic-quintic-septic nonlinearity term. To obtain meaningful results, we first defined the wave transform and applied it to the NLSE. We then derived the ordinary differential equation (ODE). We gave brief information about the new Kudryashov method (nKM) and applied it to our problem. Finally, we solved the system using Maple. Using these solutions, we obtained a bright soliton and then illustrated the graphics and analyzed the effect of the parameters of the equation on the graph of such a soliton solution.

Keywords

Optical soliton, Parameter effect, The new Kudryashov method, (3+1)-dimensional NLSE

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Details

Primary Language

English

Subjects

Mathematical Methods and Special Functions, Applied Mathematics (Other)

Journal Section

Research Article

Authors

Mehmet Fatih Uçar ^*
0000-0002-5542-2222
Türkiye

Early Pub Date

July 30, 2025

Publication Date

September 6, 2025

Submission Date

April 6, 2025

Acceptance Date

July 1, 2025

Published in Issue

Year 2025 Volume: 13 Number: 3

DOI

https://doi.org/10.36753/mathenot.1670727

IZ

https://izlik.org/JA97DK72MA

APA

Uçar, M. F. (2025). Optical Soliton Solutions of a $(3+1)$-Dimensional Nonlinear Schrödinger Equation with Cubic-Quintic-Septic Nonlinearity. Mathematical Sciences and Applications E-Notes, 13(3), 116-125. https://doi.org/10.36753/mathenot.1670727

AMA

1.Uçar MF. Optical Soliton Solutions of a $(3+1)$-Dimensional Nonlinear Schrödinger Equation with Cubic-Quintic-Septic Nonlinearity. Math. Sci. Appl. E-Notes. 2025;13(3):116-125. doi:10.36753/mathenot.1670727

Chicago

Uçar, Mehmet Fatih. 2025. “Optical Soliton Solutions of a $(3+1)$-Dimensional Nonlinear Schrödinger Equation With Cubic-Quintic-Septic Nonlinearity”. Mathematical Sciences and Applications E-Notes 13 (3): 116-25. https://doi.org/10.36753/mathenot.1670727.

EndNote

Uçar MF (September 1, 2025) Optical Soliton Solutions of a $(3+1)$-Dimensional Nonlinear Schrödinger Equation with Cubic-Quintic-Septic Nonlinearity. Mathematical Sciences and Applications E-Notes 13 3 116–125.

IEEE

[1]M. F. Uçar, “Optical Soliton Solutions of a $(3+1)$-Dimensional Nonlinear Schrödinger Equation with Cubic-Quintic-Septic Nonlinearity”, Math. Sci. Appl. E-Notes, vol. 13, no. 3, pp. 116–125, Sept. 2025, doi: 10.36753/mathenot.1670727.

ISNAD

Uçar, Mehmet Fatih. “Optical Soliton Solutions of a $(3+1)$-Dimensional Nonlinear Schrödinger Equation With Cubic-Quintic-Septic Nonlinearity”. Mathematical Sciences and Applications E-Notes 13/3 (September 1, 2025): 116-125. https://doi.org/10.36753/mathenot.1670727.

JAMA

1.Uçar MF. Optical Soliton Solutions of a $(3+1)$-Dimensional Nonlinear Schrödinger Equation with Cubic-Quintic-Septic Nonlinearity. Math. Sci. Appl. E-Notes. 2025;13:116–125.

MLA

Uçar, Mehmet Fatih. “Optical Soliton Solutions of a $(3+1)$-Dimensional Nonlinear Schrödinger Equation With Cubic-Quintic-Septic Nonlinearity”. Mathematical Sciences and Applications E-Notes, vol. 13, no. 3, Sept. 2025, pp. 116-25, doi:10.36753/mathenot.1670727.

Vancouver

1.Mehmet Fatih Uçar. Optical Soliton Solutions of a $(3+1)$-Dimensional Nonlinear Schrödinger Equation with Cubic-Quintic-Septic Nonlinearity. Math. Sci. Appl. E-Notes. 2025 Sep. 1;13(3):116-25. doi:10.36753/mathenot.1670727