Results 11 to 20 of about 198,995 (264)
Similarity Solutions to Nonlinear Diffusion/Harry Dym Fractional Equations
Advances in Mathematical Physics, 2021 By using scalar similarity transformation, nonlinear model of time-fractional diffusion/Harry Dym equation is transformed to corresponding ordinary fractional differential equations, from which a travelling-wave similarity solution of time-fractional ...
Chao Yue +3 more
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PLoS ONE, 2023 The present study computes the Lie symmetries and exact solutions of some problems modeled by nonlinear partial differential equations. The (1 + 1)-dimensional integro-differential Ito, the first integro-differential KP hierarchy, the Calogero ...
Amina Amin, Imran Naeem, Adnan Khan
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Lie symmetry and exact homotopic solutions of a non-linear double-diffusion problem
Frontiers in Physics, 2023 The Lie symmetry method is applied, and exact homotopic solutions of a non-linear double-diffusion problem are obtained. Additionally, we derived Lie point symmetries and corresponding transformations for equations representing heat and mass transfer in ...
R. A. Khan +5 more
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Similarity solutions for strong shocks in a non-ideal gas
Mathematical Modelling and Analysis, 2012 A group theoretic method is used to obtain an entire class of similarity solutions to the problem of shocks propagating through a non-ideal gas and to characterize analytically the state dependent form of the medium ahead for which the problem is ...
Rajan Arora, Amit Tomar, Ved Pal Singh
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Theoretical and Applied Mechanics Letters, 2022 The exact similarity solutions of two dimensional laminar boundary layer were obtained by Blasius in 1908, however, for two dimensional turbulent boundary layers, no Blasius type similarity solutions (special exact solutions) have ever been found. In the
Bo-Hua Sun
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Exact Solutions of the Two-Dimensional Cattaneo Model Using Lie Symmetry Transformations
Discrete Dynamics in Nature and Society, 2021 In this article, symmetry technique is utilized to obtain new exact solutions of the Cattaneo equation. The infinitesimal symmetries, linear combinations of these symmetries, and corresponding similarity variables are determined, which lead to many exact
Khudija Bibi, Khalil Ahmad
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Similarity solutions of thermal vortex rings: Vorticity–dynamics-based derivation
AIP Advances, 2023 This study derives the classical similarity solutions for the thermal vortex ring, originally deduced by Scorer [J. Fluid Mech. 2, 583–594 (1957)] based on dimensional analysis from basic principles of vorticity dynamics. Derivations are performed by two
Jun-Ichi Yano
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Partial Differential Equations in Applied Mathematics, 2022 In the present investigation, an attempt is performed to analyse the existence of multiple exact solutions for magnetohydrodynamic flows of second-grade and Walter’s B fluids due continuously contracting flat sheet with partial slip condition at the ...
Anil Kumar Gautam +5 more
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On similarity and pseudo-similarity solutions of Falkner–Skan boundary layers [PDF]
Fluid Dynamics Research, 2006 The present work deals with the two-dimensional incompressible,laminar, steady-state boundary layer equations. First, we determinea family of velocity distributions outside the boundary layer suchthat these problems may have similarity solutions. Then, we examenin detail new exact solutions, called Pseudo--similarity, where the external velocity varies
Guedda, Mohamed, Hammouch, Zakia
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Similarity inner solutions for the Pulsar equation [PDF]
Mathematical Methods in the Applied Sciences, 2019 Lie symmetries are applied to classify the source of the magnetic field for the Pulsar equation near to the surface of the neutron star. We find that there are six possible different admitted Lie algebras. We apply the corresponding Lie invariants to reduce the Pulsar equation close to the surface to an ordinary differential equation.
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