article · Physics of Fluids
This study investigates the mathematical properties of a (3 + 1)-dimensional Boussinesq-type equation describing wave behaviour in fluid mediums. Using computer algebra in Mathematica, the research confirms the Painlevé integrability of the model. Through Hirota's bilinear technique, the analysis determines key dispersion relations and phase shifts, allowing the derivation of multiple soliton solutions. In addition, symbolic computation in Maple is used to construct a diverse set of lump solutions. The work also uncovers several other exact solutions, including kink, periodic, singular, and rational wave structures. Together, these analytical solutions demonstrate the dynamic versatility of the governing equation. The mathematical results provide a framework for examining the formation and movement of nonlinear waves, supporting theoretical understanding in areas such as ocean surface dynamics, fluid mechanics, plasma physics, and optical fibres.
Nonlinear waves govern critical behaviours in oceanography, telecommunications, and fluid systems. Solving complex equations like the (3 + 1)-dimensional Boussinesq equation provides exact mathematical expressions for intricate wave formations, such as solitons and lumps. These analytical insights help physicists and engineers model energy transport and wave stability in real-world media, including optical fibres and turbulent water surfaces.
This research represents early-stage fundamental mathematical modelling. While it identifies potential relevance to wave propagation in optical fibres, ocean surface monitoring, and plasma systems, it does not present an applied technology or prototype. Potential end users include theoretical researchers and simulation software developers in fluid mechanics and photonics, but direct commercial deployment would require subsequent applied validation and engineering integration.
AI-generated from the published abstract. Always read the original work before citing.
This work examines the Painlevé integrability of a (3 + 1)-dimensional Boussinesq-type equation. Using the Mathematica program, we rigorously establish Painlevé's integrability for the suggested problem. By utilizing Hirota's bilinear technique, we obtain the dispersion relations and phase shifts, which enable us to derive multiple soliton solutions. In addition, we systematically derive a wide range of lump solutions using the Maple symbolic computation. The investigation extends to encompass a variety of exact solutions with distinct structural features, including kink, periodic, singular, and rational solutions. This comprehensive analysis illustrates the profound richness of the model's dynamics and its potential to elucidate diverse nonlinear wave phenomena across various physical contexts. Therefore, the results that we will obtain play a vital role in understanding the mechanism of generation and propagation of many mysterious phenomena that arise in various scientific fields, including plasma physics, fluid mechanics, and the propagation of waves on the surfaces of seas and oceans to optical fibers.
This page summarises published work. The authoritative version sits with the publisher.
DOI: 10.1063/5.0194071
Is something wrong with this record? Report it or request removal.
Discussion
Have you built on this work, tried to replicate it, or seen it applied in practice? Share what you know. Verified researchers and MARATTO™ domain experts can open a discussion, and any member can reply. Contributions are reviewed before they appear.
No discussion yet. Open the first thread.
New to MARATTO™? Create a free account.
