Analyzing the time-fractional (3 + 1)-dimensional nonlinear Schrödinger equation: a new Kudryashov approach and optical solutions

• Published in: International journal of computer mathematics Vol. 101; no. 5; pp. 524 - 537
• Main Author: Murad, Muhammad Amin Sadiq
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 03.05.2024; Taylor & Francis Ltd
• Subjects: 78-10; conformable fractional order derivative; Exact solutions; Fractional calculus; Laser beams; Nonlinear differential equations; Nonlinear optics; Nonlinear systems; Optical pulses; optical solutions; Partial differential equations; Phase modulation; Pulse propagation; Schrodinger equation; Solitary waves; the new Kudryashov approach; The time-fractional (3 + 1)-dimensional nonlinear Schrödinger
• ISSN: 0020-7160; 1029-0265
• DOI: 10.1080/00207160.2024.2351110

The paper focuses on investigating the time-fractional (3 + 1)-dimensional cubic and quantic nonlinear Schrödinger equation. We adopt the novel Kudryashov method to generate a distinct class of optical solutions for the current conformable fractional derivative problem. Our method explores various solution forms, including dark, wave, mixed dark-bright, and singular solutions. The soliton solutions we construct are visually represented to illustrate the influence of the fractional order derivative. Further, we elucidate the influence of solution parameters on the wave envelope, providing clear interpretations through 2D graphics presentations. The results underscore the efficacy of our approach in discovering exact solutions for nonlinear partial differential equations, especially in cases where alternative methods prove ineffective. The significance of the present paper lies in its contribution to advancing the understanding of the behavior of optical solutions in nonlinear systems, providing valuable insights for both theoretical and practical applications. In the field of nonlinear optics, this equation can describe the propagation of optical pulses in nonlinear media. It helps in understanding the behavior of intense laser beams as they propagate through materials exhibiting nonlinear optical effects such as self-focusing, self-phase modulation, and optical solitons.