Lie symmetry analysis of a class of thermal conduction models

Biyadi, Houda; Amtout, Tarik; Er‐Riani, Mustapha; Jarroudi, Mustapha El

doi:10.12988/ams.2019.99136

Cited by 1 publication

(2 citation statements)

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“…We use the traveling wave transformation u(t, x) = U(X), X = x − ct, where c represents wave velocity. By making use of this transformation, the nonlinear partial differential equation (5.3) is transformed to the following ordinary differential equation 3) , . .…”

Section: Second Case When F(u) = F 0 (1 − Bu)mentioning

confidence: 99%

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Lie group classification of the nonlinear transmission line model and exact traveling wave solutions

Amtout¹,

Er-Riani²,

Jarroud³

2022

J. Nonlinear Sci. Appl.

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A nonlinear transmission line (NLTL) model is very essential tools in understanding of propagation of electrical solitons which can propagate in the form of voltage waves in nonlinear dispersive media. These models are often formulated using nonlinear partial differential equations. One of the basic tools available to study these equations are numerical methods such as finite difference method, finite element method, etc, have been developed for nonlinear partial differential equations. These methods require a great amount of time and memory due to the discretization and usually the effect of round-off error causes loss of accuracy in the results. So in this paper, we use one of the most famous analytical methods the Lie group analysis due to Sophus Lie. One of the advantages of this approach is that requires only algebraic calculations. The main aim of this study is to explore the nonlinear transmission line model with arbitrary capacitor's voltage dependence, through the use of Lie group classification, we show that the specifying form of arbitrary capacitor's voltage are power law nonlinearity, exponential law nonlinearity and constant capacitance. The exact solutions and similarity reductions generated from the symmetries are also provided. Furthermore, translational symmetries were utilized to find a family of traveling wave solutions via the tanh-method of the governing nonlinear problem.

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Section: Second Case When F(u) = F 0 (1 − Bu)mentioning

confidence: 99%

“…For the large applications of this method in engineering and physics, many authors (see [2,3,7,8]) explained the applications of Lie symmetries to partial or fractional partial differential equations.…”

Section: Introductionmentioning

confidence: 99%