Some New Families of Exact Solitary Wave Solutions for Pseudo-Parabolic Type Nonlinear Models

The objective of the current study is to provide a variety of families of soliton solutions to pseudo-parabolic equations that arise in nonsteady flows, hydrostatics, and seepage of fluid through fissured material. We investigate a class of such equations, including the one-dimensional Oskolkov (1D...

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Published inJournal of mathematics (Hidawi) Vol. 2024; pp. 1 - 19
Main Authors Hussain, Akhtar, Ali, Hassan, Usman, M., Zaman, F. D., Park, Choonkil
Format Journal Article
LanguageEnglish
Published Cairo Hindawi 2024
Hindawi Limited
Subjects
Hydrostatics
Partial differential equations
Physics
Polynomials
Seepage
Solitary waves
Traveling waves
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Summary:The objective of the current study is to provide a variety of families of soliton solutions to pseudo-parabolic equations that arise in nonsteady flows, hydrostatics, and seepage of fluid through fissured material. We investigate a class of such equations, including the one-dimensional Oskolkov (1D OSK), the Benjamin-Bona-Mahony (BBM), and the Benjamin-Bona-Mahony-Peregrine-Burgers (BBMPB) equation. The Exp (-ϕξ)-expansion method is used for new hyperbolic, trigonometric, rational, exponential, and polynomial function-based solutions. These solutions of the pseudo-parabolic class of partial differential equations (PDEs) studied here are new and novel and have not been reported in the literature. These solutions depict the hydrodynamics of various soliton shapes that can be utilized to study the nature of traveling wave solutions of other nonlinear PDE’s.
ISSN:2314-4629
2314-4785
DOI:10.1155/2024/5762147