Journal
OPEN PHYSICS
Volume 20, Issue 1, Pages 778-794Publisher
DE GRUYTER POLAND SP Z O O
DOI: 10.1515/phys-2022-0071
Keywords
improved Bernoulli subequation function method; the new auxiliary equation method; the variant Boussinesq equation; exact solutions; soliton
Categories
Funding
- National Natural Science Foundation of China [71601072]
- Key Scientific Research Project of Higher Education Institutions in Henan Province of China [20B110006]
- Fundamental Research Funds for the Universities of Henan Province
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The improved Bernoulli subequation function (IBSEF) method and the new auxiliary equation (NAE) technique are introduced to establish general and specific solutions. The physical significance of the obtained solutions is speculated by depicting the 3D profiles and interpreting the physical incidents. The obtained solutions and graphical representations visualize the dynamics of the phenomena.
The variant Boussinesq equation has significant application in propagating long waves on the surface of the liquid layer under gravity action. In this article, the improved Bernoulli subequation function (IBSEF) method and the new auxiliary equation (NAE) technique are introduced to establish general solutions, some fundamental soliton solutions accessible in the literature, and some archetypal solitary wave solutions that are extracted from the broad-ranging solution to the variant Boussinesq wave equation. The established soliton solutions are knowledgeable and obtained as a combination of hyperbolic, exponential, rational, and trigonometric functions, and the physical significance of the attained solutions is speculated for the definite values of the included parameters by depicting the 3D profiles and interpreting the physical incidents. The wave profile represents different types of waves associated with the free parameters that are related to the wave number and velocity of the solutions. The obtained solutions and graphical representations visualize the dynamics of the phenomena and build up the mathematical foundation of the wave process in dissipative and dispersive media. It turns out that the IBSEF method and the NAE are powerful and might be used in further works to find novel solutions for other types of nonlinear evolution equations ascending in physical sciences and engineering.
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