Optical solitons and bifurcation analysis in the cubic quintic septic nonic nonlinear Schrödinger equation using modified extended direct algebraic method

Articles in Press

Document Type : Research Paper

Authors

1 Guangdong Provincial Key Laboratory of Durability for Marine Civil Engineering, Shenzhen University, Shenzhen 518060, China.

2 Department of Physics and Engineering Math, The Higher Institute of Engineering, El Shorouk Academy, Cairo, Egypt.

3 Department of Mathematics, Faculty of Science, Al Azhar University, Cairo, Egypt.

4 Department of Mathematics, Faculty of Science, Luxor University, Taiba, Luxor, Egypt.

10.22034/cmde.2025.68670.3342

Abstract

This study investigates the nonlinear Schr\"{o}dinger equation characterized by constant coefficients in a cubic–quintic–septic–nonic medium. By employing the modified extended direct algebraic method, a diverse range of analytical solutions is derived, including bright, dark, and mixed dark–bright soliton solutions, as well as singular structures. Additionally, the work presents periodic, exponential, rational, Jacobi elliptic, and Weierstrass elliptic solutions. To illustrate the physical characteristics of the obtained solutions, two-dimensional, three-dimensional, and contour plots are generated for specific parameter choices. A detailed bifurcation analysis is conducted to examine the system’s stability and dynamic transitions, supported by phase portraits and sensitivity analysis with respect to key parameters.

Keywords

Main Subjects

Computational Methods for Differential Equations

Articles in Press, Accepted Manuscript
Available Online from 05 January 2026

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History

  • Receive Date: 15 August 2025
  • Revise Date: 20 December 2025
  • Accept Date: 05 January 2026

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