https://doi.org/10.1140/epjp/s13360-024-05442-2
Regular Article
Exploring the impact of multiplicative white noise on novel soliton solutions with the perturbed Triki–Biswas equation
1
Department of Physics and Engineering Mathematics, Higher Institute of Engineering, El–Shorouk Academy, Cairo, Egypt
2
Department of Mathematics, College of Science, Taif University, P.O. Box 11099, 21944, Taif, Saudi Arabia
3
Department of Computer Engineering, Biruni University, 34010, Istanbul, Turkey
4
Mathematics Research Center, Near East University, 99138, Nicosia, Cyprus
d yakupyildirim110@gmail.com, yyildirim@biruni.edu.tr
Received:
5
May
2024
Accepted:
10
July
2024
Published online:
25
July
2024
This study examines the effects of multiplicative white noise on soliton perturbations governed by the Triki–Biswas equation for the first time. Triki–Biswas equation advances research on ultrashort pulse propagation in optical fibers. It modifies the nonlinear Schrödinger equation to describe the behavior of femtosecond pulses more accurately in optical media, becoming a critical tool in the field. The paper employs two innovative methods, the enhanced direct algebraic method and the new projective Riccati equations method to uncover a broad range of soliton solutions, including bright, dark, and singular solitons. The solutions are expressed in terms of Jacobi elliptic functions and exhibit a transition to soliton-type solutions as the elliptic modulus approaches unity. This investigation is the first of its kind to explore the effects of multiplicative white noise within this context, providing new perspectives and methodologies for future research in the field. The study sheds light on previously unexplored aspects of multiplicative white noise and contributes significantly to the body of knowledge in soliton theory and its application to optical fiber technology.
© The Author(s) 2024
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