Evolution of planar and cylindrically symmetric magneto-acoustic waves in a van der Waals fluid |
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| Affiliation: | 1. Department of Mathematics, City University of Science and IT, Peshawar, 25000, Pakistan;2. College of Aeronautical Engineering, National University of Sciences and Technology (NUST), Sector H-12, Islamabad 44000, Pakistan;3. Department of Basic Sciences, College of Science and Theoretical Studies, Saudi Electronic University, Riyadh, Saudi Arabia;4. Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia;5. Higher Education Archives & Libraries Department KP, Govt. Superior Science College, Peshawar, Pakistan |
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| Abstract: | We consider a quasilinear system of partial differential equations (PDEs) governing the one-dimensional unsteady planar and cylindrically symmetric motion of an electrically conducting van der Waals fluid permeated with a transverse magnetic field. An asymptotic method is used to derive an evolution equation that governs the wave amplitude in the far field. Our main objective is to study the evolution equation, and to investigate as to how the presence of magnetic field and geometrical spreading (in cylindrical case) along with the cubic nonlinearity, inherently present in the system, influence the wave structure that finally develops. |
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| Keywords: | Magneto-acoustic waves van der Waals fluids Cubic nonlinearity Expansion shocks |
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