Investigations of soliton structures and dynamical behaviors of the Westervelt equation with two analytical techniques

The study of nonlinear partial differential equations is a crucial area of scientific research to understand fundamental properties and common characteristics of nonlinear phenomena. This research focuses on the Westervelt equation and various new soliton structures, which are systematically derived...

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Main Authors: Md. Masudar Rahman, S. M. Rayhanul Islam, Ashabul Hoque
Format: Article
Language:English
Published: AIP Publishing LLC 2025-05-01
Series:AIP Advances
Online Access:http://dx.doi.org/10.1063/5.0271307
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author Md. Masudar Rahman
S. M. Rayhanul Islam
Ashabul Hoque
author_facet Md. Masudar Rahman
S. M. Rayhanul Islam
Ashabul Hoque
author_sort Md. Masudar Rahman
collection DOAJ
description The study of nonlinear partial differential equations is a crucial area of scientific research to understand fundamental properties and common characteristics of nonlinear phenomena. This research focuses on the Westervelt equation and various new soliton structures, which are systematically derived using improved F-expansion and unified approaches. To verify the physical relevance of the results, three-dimensional (3D) and two-dimensional (2D) combined plots are generated by selecting appropriate parameter values, offering more profound insights into the obtained wave solutions. By changing the values of the parameters, we get different types of 3D wave profiles. In addition, the influence of sound diffusivity on the Westervelt equation is examined using 2D-combined plots. We also compare the solutions obtained for our schemes and our solutions with those in the previous literature. Furthermore, the methods employed are efficient and reliable for constructing novel soliton wave solutions in nonlinear physical systems. The findings of this research are expected to have significant applications in medical science, including transducers, contrast agents, pulse compression, beam shaping, tissue harmonic imaging, blood flow and tissue motion measurement techniques, three-dimensional imaging, and several other fields.
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spelling doaj-art-843eea0ed92b49e4a5de2b2588f20b072025-08-20T03:19:43ZengAIP Publishing LLCAIP Advances2158-32262025-05-01155055234055234-1210.1063/5.0271307Investigations of soliton structures and dynamical behaviors of the Westervelt equation with two analytical techniquesMd. Masudar Rahman0S. M. Rayhanul Islam1Ashabul Hoque2Department of Mathematics, Bangladesh Army University of Engineering and Technology, Natore 6431, BangladeshDepartment of Mathematics, Pabna University of Science and Technology, Pabna 6600, BangladeshDepartment of Mathematics, University of Rajshahi, Rajshahi 6205, BangladeshThe study of nonlinear partial differential equations is a crucial area of scientific research to understand fundamental properties and common characteristics of nonlinear phenomena. This research focuses on the Westervelt equation and various new soliton structures, which are systematically derived using improved F-expansion and unified approaches. To verify the physical relevance of the results, three-dimensional (3D) and two-dimensional (2D) combined plots are generated by selecting appropriate parameter values, offering more profound insights into the obtained wave solutions. By changing the values of the parameters, we get different types of 3D wave profiles. In addition, the influence of sound diffusivity on the Westervelt equation is examined using 2D-combined plots. We also compare the solutions obtained for our schemes and our solutions with those in the previous literature. Furthermore, the methods employed are efficient and reliable for constructing novel soliton wave solutions in nonlinear physical systems. The findings of this research are expected to have significant applications in medical science, including transducers, contrast agents, pulse compression, beam shaping, tissue harmonic imaging, blood flow and tissue motion measurement techniques, three-dimensional imaging, and several other fields.http://dx.doi.org/10.1063/5.0271307
spellingShingle Md. Masudar Rahman
S. M. Rayhanul Islam
Ashabul Hoque
Investigations of soliton structures and dynamical behaviors of the Westervelt equation with two analytical techniques
AIP Advances
title Investigations of soliton structures and dynamical behaviors of the Westervelt equation with two analytical techniques
title_full Investigations of soliton structures and dynamical behaviors of the Westervelt equation with two analytical techniques
title_fullStr Investigations of soliton structures and dynamical behaviors of the Westervelt equation with two analytical techniques
title_full_unstemmed Investigations of soliton structures and dynamical behaviors of the Westervelt equation with two analytical techniques
title_short Investigations of soliton structures and dynamical behaviors of the Westervelt equation with two analytical techniques
title_sort investigations of soliton structures and dynamical behaviors of the westervelt equation with two analytical techniques
url http://dx.doi.org/10.1063/5.0271307
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AT ashabulhoque investigationsofsolitonstructuresanddynamicalbehaviorsofthewesterveltequationwithtwoanalyticaltechniques