Abundant different types of soliton solutions for fractional modified KdV equation using auxiliary equation method.

Akhtar Hussain, Tarek F Ibrahim, Fathea M Osman Birkea, M Sh Yahya, Abaker A Hassaballa, Herbert Mukalazi

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Article in Scientific reports, 2025. 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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6 authors.

Akhtar HussainDepartment of Mathematics, University of Management and Technology, Lahore, 54770, Pakistan.

Tarek F IbrahimDepartment of Mathematics, Faculty of Sciences, Mansoura University, Mansoura, Egypt.

Fathea M Osman BirkeaDepartment of Mathematics, Faculty of Science, Northern Border University, Arar, Saudi Arabia.

M Sh YahyaDepartment of Mathematics, College of Sciences, King Khalid University, Abha, Saudi Arabia.

Abaker A HassaballaCenter for Scientific Research and Entrepreneurship, Northern Border University, Arar, 73213, Saudi Arabia.

Herbert MukalaziDepartment of Mathematics and Statistics, Kyambogo University, Kampala, Uganda. hmukalazi@kyu.ac.ug.

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Abstract

This research focuses on investigating soliton solutions for the space-time fractional modified third-order Korteweg-de Vries equation using the auxiliary equation method. The Korteweg-de Vries equation is renowned for its application in modeling shallow-water waves, oceanographic dynamics, and ion-acoustic waves in plasma. By employing a traveling wave transformation, the fractional-order partial differential equation is converted into a nonlinear ordinary differential equation. This study used conformable derivatives to solve the fractional differential equation. Soliton solutions, including bright, dark, singular, periodic singular, combined bright-dark, and combined dark-singular forms, are derived through the application of auxiliary equation method to the reduced equation.

Indexed as

Auxiliary equation methodConformal derivativeKorteweg-de Vries equationOptical solitonsShallow water waves

Identifiers

PMID41372227

DOI10.1038/s41598-025-26779-3

PMCPMC12696082

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