<abstract xmlns="http://www.w3.org/1999/xhtml">
<p>Our investigation delves into a specific category of nonlinear pseudo-parabolic partial differential equations (PDEs) that emerges from physical models. This set of equations includes the one-dimensional (1D) Oskolkov equation, the Benjamin-Bona-Mahony-Peregrine-Burgers (BBMPB) equation, the generalized hyperelastic rod wave (HERW) equation, and the Oskolkov Benjamin Bona Mahony Burgers (OBBMB) equation. We employ the new extended direct algebraic (NEDA) method to tackle these equations. The NEDA method serves as a powerful tool for our analysis, enabling us to obtain solutions grounded in various mathematical functions, such as hyperbolic, trigonometric, rational, exponential, and polynomial functions. As we delve into the physical implications of these solutions, we uncover complex structures with well-known characteristics. These include entities like dark, bright, singular, combined dark-bright solitons, dark-singular-combined solitons, solitary wave solutions, and others.</p>
</abstract>

Our investigation delves into a specific category of nonlinear pseudo-parabolic partial differential equations (PDEs) that emerges from physical models. This set of equations includes the one-dimensional (1D) Oskolkov equation, the Benjamin-Bona-Mahony-Peregrine-Burgers (BBMPB) equation, the generalized hyperelastic rod wave (HERW) equation, and the Oskolkov Benjamin Bona Mahony Burgers (OBBMB) equation. We employ the new extended direct algebraic (NEDA) method to tackle these equations. The NEDA method serves as a powerful tool for our analysis, enabling us to obtain solutions grounded in various mathematical functions, such as hyperbolic, trigonometric, rational, exponential, and polynomial functions. As we delve into the physical implications of these solutions, we uncover complex structures with well-known characteristics. These include entities like dark, bright, singular, combined dark-bright solitons, dark-singular-combined solitons, solitary wave solutions, and others.

New closed form solutions of some nonlinear pseudo-parabolic models via a new extended direct algebraic method

Abdus Salam School of Mathematical Sciences

International Journal of Mathematics and Computer in Engineering

This work is licensed under the Creative Commons Attribution 4.0 International License.

Our investigation delves into a specific category of nonlinear pseudo-parabolic partial differential equations (PDEs) that emerges from physical models. This...

New closed form solutions of some nonlinear pseudo-parabolic models via a new extended direct algebraic method

Article Category: Original Study

Published Online: Oct 31, 2023

Page range: 35 - 58

Received: Aug 11, 2023

Accepted: Sep 11, 2023

DOI: https://doi.org/10.2478/ijmce-2024-0004

Keywords
Benjamin-Bona-Mahony-Peregrine equation, generalized hyper elastic rod wave equation, pseudo-parabolic class, new extended direct algebraic method

© 2024 Akhtar Hussain et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

New closed form solutions of some nonlinear pseudo-parabolic models via a new extended direct algebraic method

Article Category: Original Study

Published Online: Oct 31, 2023

Page range: 35 - 58

Received: Aug 11, 2023

Accepted: Sep 11, 2023

DOI: https://doi.org/10.2478/ijmce-2024-0004

KeywordsBenjamin-Bona-Mahony-Peregrine equation, generalized hyper elastic rod wave equation, pseudo-parabolic class, new extended direct algebraic method

© 2024 Akhtar Hussain et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Keywords
Benjamin-Bona-Mahony-Peregrine equation, generalized hyper elastic rod wave equation, pseudo-parabolic class, new extended direct algebraic method