Exploring the new classes of optical soliton solutions with diverse structure for the (2+1)-dimensional paraxial equation in fiber optics via two analytical methods.

Ibrahim Sani Ibrahim, Jamilu Sabi'u, Mujahid Iqbal, Surajo Sulaiman, Weam Gaoud Alghabban, Soumaya Gouadria, Nazar Mohammad Nazar

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Article in Scientific reports, 2026. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 1 paper.

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Optical soliton solutions of the nonlinear coupled Konno-Oono system by using the new analytical approach and modulation instability analysis.Scientific reports · 2026
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Ibrahim Sani IbrahimDepartment of Mathematics, Northwest University, Kano, Kabuga Road, 700282, Kano, Nigeria.

Jamilu Sabi'uDepartment of Mathematics, King Fahd University of Petroleum and Minerals, Dhahran, 31261, Saudi Arabia.

Mujahid IqbalCollege of Information Science and Technology, Dalian Maritime University, Dalian, 116026, Liaoning, People's Republic of China. mujahidiqbal399@gmail.com.

Surajo SulaimanDepartment of Mathematics, Northwest University, Kano, Kabuga Road, 700282, Kano, Nigeria.

Weam Gaoud AlghabbanDepartment of Computer Science, Alwajh University College, University of Tabuk, 71491, Tabuk, Saudi Arabia.

Soumaya GouadriaDepartment of Physics, College of Science, Princess Nourah bint Abdualrahman University, P. O. Box 84428, 11671, Riyadh, Saudi Arabia.

Nazar Mohammad NazarDepartment of Mathematics, Faculty of Science, University of Nangarhar, 2601, Jalalabad, Afghanistan. n.moh@nu.edu.af.

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6 · The paper itself

Abstract

This research explores the analytical soliton solutions of the dimensionless time-dependent paraxial equation (DTPE). We applied the improved Sardar sub-equation and improved Riccati equation analytical techniques to develop numerous soliton solutions for the DTPE, providing insights into the behavior of optical solitons in nonlinear evolution equations. The two techniques are applied for the first time to generate vigorous solutions to the DTPE. Numerous types of exponential, trigonometric, hyperbolic, dark, periodic, anti-kink, peakon, kink, and bright soliton solutions are obtained for DTPE. Although constructing an effective scheme to solve the DTPE has been our primary aim. Moreover, the obtained analytical solutions offer a useful foundation for comprehending the complex dynamics of optical solitons in nonlinear evolution equations, enabling enhancements in different applications that include signal processing, optical communication, beam shaping, Gaussian beams, lenses and mirrors, optical fibers, and predicting beam behaviors.

Indexed as

Improved Riccati equation methodImproved Sardar sub-equation methodNonlinear paraxial wave equationSoliton solutionsSymbolic computation

Identifiers

PMID41796166

DOI10.1038/s41598-026-42607-8

PMCPMC13087239

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