Investigations of soliton structures and dynamical behaviors of the Westervelt equation with two analytical techniques
Source abstract
Abstract
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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Research context
OpenAlex topics: Nonlinear Waves and Solitons · Numerical methods for differential equations · Fractional Differential Equations Solutions
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
Affiliations
Department of Mathematics, Bangladesh Army University of Engineering and Technology 1 , Natore 6431,
Department of Mathematics, Pabna University of Science and Technology 2 , Pabna 6600,
Department of Mathematics, University of Rajshahi 3 , Rajshahi 6205,
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