Soliton‐Like Solutions and Determination of Unique Physical Problems for the Nonclassical Sobolev‐Type Equation in Fluid Dynamics

ABSTRACT The current study deals with Sobolev‐type equations, which are utilized in numerous disciplines, including thermodynamics, fluid dynamics, ecology, and soil mechanics. In the present manuscript, we investigate Sobolev‐type models by means of the modified auxiliary equation (MAE) and the new modified extended direct algebraic (NMEDA) approaches. The results obtained in this report include families of analytical solutions, such as singular solutions, mixed singular solutions, trigonometric solutions, mixed dark‐bright solutions, shock solutions, and mixed periodic solutions. The stability of the model has been investigated herein. Additionally, a variety of physical problems were selected to provide a range of solutions. Graphs in 2D, 3D, and line formats corresponding to various parameter values are plotted.

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Publication Details

Journal
Mathematical Methods in the Applied Sciences
Published
2025-12-03
DOI
https://doi.org/10.1002/mma.70366
Primary Topic
Nonlinear Waves and Solitons
Type
article
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article

Soliton‐Like Solutions and Determination of Unique Physical Problems for the Nonclassical Sobolev‐Type Equation in Fluid Dynamics

Muhammad Zafarullah Baber, Nauman Ahmed, Muhammad Waqas Yasin, Jorge E. Macías‐Díaz et al.
Mathematical Methods in the Applied Sciences
Nonlinear Waves and Solitons
article

Soliton‐Like Solutions and Determination of Unique Physical Problems for the Nonclassical Sobolev‐Type Equation in Fluid Dynamics

Muhammad Zafarullah Baber, Nauman Ahmed, Muhammad Waqas Yasin, Jorge E. Macías‐Díaz, Siegfried Macías, Muhammad Ahmad, Tahir Shahzad
article en

Abstract

ABSTRACT The current study deals with Sobolev‐type equations, which are utilized in numerous disciplines, including thermodynamics, fluid dynamics, ecology, and soil mechanics. In the present manuscript, we investigate Sobolev‐type models by means of the modified auxiliary equation (MAE) and the new modified extended direct algebraic (NMEDA) approaches. The results obtained in this report include families of analytical solutions, such as singular solutions, mixed singular solutions, trigonometric solutions, mixed dark‐bright solutions, shock solutions, and mixed periodic solutions. The stability of the model has been investigated herein. Additionally, a variety of physical problems were selected to provide a range of solutions. Graphs in 2D, 3D, and line formats corresponding to various parameter values are plotted.

Mathematical Methods in the Applied SciencesVol. 49(5)
Tallinn University of Technology (EE), Shanghai University (CN), SHOWA Medical University (JP), University of Lahore (PK), University of Engineering and Technology Lahore (PK), University of Shanghai for Science and Technology (CN), University of Sargodha (PK), Autonomous University of Aguascalientes (MX), Tallinn University (EE), Lahore University of Management Sciences (PK), New York University Shanghai (CN), Jadara University (JO)
Openalex Percentile: Top 70%
Nonlinear Waves and Solitons
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