The Experts below are selected from a list of 294 Experts worldwide ranked by ideXlab platform
A J Hariton - One of the best experts on this subject based on the ideXlab platform.
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Invariant solutions of a nonlinear Wave Equation with a small dissipation obtained via approximate symmetries
Ricerche di Matematica, 2020Co-Authors: A M Grundland, A J HaritonAbstract:In this paper, it is shown how a combination of approximate symmetries of a nonlinear Wave Equation with small dissipations and singularity analysis provides exact analytic solutions. We perform the analysis using the Lie symmetry algebra of this Equation and identify the conjugacy classes of the one-dimensional subalgebras of this Lie algebra. We show that the subalgebra classification of the integro-differential form of the nonlinear Wave Equation is much larger than the one obtained from the original Wave Equation. A systematic use of the symmetry reduction method allows us to find new invariant solutions of this Wave Equation.
Dumitru Baleanu - One of the best experts on this subject based on the ideXlab platform.
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Approximate Solutions of the Damped Wave Equation and Dissipative Wave Equation in Fractal Strings
Fractal and Fractional, 2019Co-Authors: Dumitru Baleanu, Hassan Kamil JassimAbstract:In this paper, we apply the local fractional Laplace variational iteration method (LFLVIM) and the local fractional Laplace decomposition method (LFLDM) to obtain approximate solutions for solving the damped Wave Equation and dissipative Wave Equation within local fractional derivative operators (LFDOs). The efficiency of the considered methods are illustrated by some examples. The results obtained by LFLVIM and LFLDM are compared with the results obtained by LFVIM. The results reveal that the suggested algorithms are very effective and simple, and can be applied for linear and nonlinear problems in sciences and engineering.
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damped Wave Equation and dissipative Wave Equation in fractal strings within the local fractional variational iteration method
Fixed Point Theory and Applications, 2013Co-Authors: Xiaojun Yang, Dumitru Baleanu, Hossein JafariAbstract:In this paper, the local fractional variational iteration method is given to handle the damped Wave Equation and dissipative Wave Equation in fractal strings. The approximation solutions show that the methodology of local fractional variational iteration method is an efficient and simple tool for solving mathematical problems arising in fractal Wave motions. MSC: 74H10; 35L05; 28A80
A M Grundland - One of the best experts on this subject based on the ideXlab platform.
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Invariant solutions of a nonlinear Wave Equation with a small dissipation obtained via approximate symmetries
Ricerche di Matematica, 2020Co-Authors: A M Grundland, A J HaritonAbstract:In this paper, it is shown how a combination of approximate symmetries of a nonlinear Wave Equation with small dissipations and singularity analysis provides exact analytic solutions. We perform the analysis using the Lie symmetry algebra of this Equation and identify the conjugacy classes of the one-dimensional subalgebras of this Lie algebra. We show that the subalgebra classification of the integro-differential form of the nonlinear Wave Equation is much larger than the one obtained from the original Wave Equation. A systematic use of the symmetry reduction method allows us to find new invariant solutions of this Wave Equation.
Yanghua Wang - One of the best experts on this subject based on the ideXlab platform.
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Generalized viscoelastic Wave Equation
Geophysical Journal International, 2015Co-Authors: Yanghua WangAbstract:S U M M A R Y This paper presents a generalized Wave Equation which unifies viscoelastic and pure elastic cases into a single Wave Equation. In the generalized Wave Equation, the degree of viscoelasticity varies between zero and unity, and is defined by a controlling parameter. When this viscoelastic controlling parameter equals to 0, the viscous property vanishes and the generalized Wave Equation becomes a pure elastic Wave Equation. When this viscoelastic controlling parameter equals to 1, it is the Stokes Equation made up of a stack of pure elastic and Newtonian viscous models. Given this generalized Wave Equation, an analytical solution is derived explicitly in terms of the attenuation and the velocity dispersion. It is proved that, for any given value of the viscoelastic controlling parameter, the attenuation component of this generalized Wave Equation perfectly satisfies the power laws of frequency. Since the power laws are the fundamental characteristics in physical observations, this generalized Wave Equation can well represent seismic Wave propagation through subsurface media.
Hossein Jafari - One of the best experts on this subject based on the ideXlab platform.
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damped Wave Equation and dissipative Wave Equation in fractal strings within the local fractional variational iteration method
Fixed Point Theory and Applications, 2013Co-Authors: Xiaojun Yang, Dumitru Baleanu, Hossein JafariAbstract:In this paper, the local fractional variational iteration method is given to handle the damped Wave Equation and dissipative Wave Equation in fractal strings. The approximation solutions show that the methodology of local fractional variational iteration method is an efficient and simple tool for solving mathematical problems arising in fractal Wave motions. MSC: 74H10; 35L05; 28A80
