Riccati-based analytical framework for solving the potential Korteweg-de Vries equation.

Yousef Jawarneh, Safyan Mukhtar, Safiqul Islam, Yaouba Amadou

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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. Not yet cited in PubMed.

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4 authors.

Yousef JawarnehDepartment of Mathematics, College of Science, University of Ha'il, Ha'il, 2440, Saudi Arabia.

Safyan MukhtarDepartment of Mathematics and Statistics, College of Science, King Faisal University, P.O. Box 400, Al Ahsa, 31982, Saudi Arabia. smahmad@kfu.edu.sa.

Safiqul IslamDepartment of Mathematics and Statistics, College of Science, King Faisal University, P.O. Box 400, Al Ahsa, 31982, Saudi Arabia.

Yaouba AmadouDepartment of Physics, Faculty of Science, The University of Maroua, P.O. Box 814, Maroua, Cameroon. yaoubamadou4@gmail.com.

Funding

Safyan Mukhtar This work was supported by the Deanship of Scientific Research, Vice Presidency for Graduate Studies and Scientific Research, King Faisal University, Saudi Arabia (Grant No. KFU262102).

6 · The paper itself

Abstract

This paper investigates the potential KdV equation by applying the Riccati-based Modified Extended Simple Equation Method (RMESEM). Through a suitable traveling wave transformation, the governing nonlinear partial differential equation is converted into an ordinary differential equation, which is then analyzed using an extended Riccati framework. As a result, several families of exact traveling wave solutions are derived in explicit analytical form. The obtained solutions include solitary wave, periodic, rational, hyperbolic, and trigonometric structures under different parameter conditions. The validity of the derived solutions is confirmed through direct substitution into the original model. In addition, the influence of the involved parameters on the wave behavior is discussed to illustrate the physical significance of the solutions. The present approach provides a systematic and effective technique for constructing exact solutions of nonlinear evolution equations arising in mathematical physics and related applied sciences.

Indexed as

Exact analytical solutionsNonlinear differential equationsNonlinear wave solutionsPeriodic solutionsPotential KdV equationRiccati-based Modified Extended Simple Equation MethodSoliton solutions

Identifiers

PMID42289530

DOI10.1038/s41598-026-56875-x

PMCPMC13527118

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