Group classification and conservation laws of nonlinear filtration equation with a small parameter

2014 ◽  
Vol 19 (2) ◽  
pp. 364-370 ◽  
Author(s):  
A.A. Alexandrova ◽  
N.H. Ibragimov ◽  
V.O. Lukashchuk
Keyword(s):  
Small Parameter ◽  
Conservation Laws ◽  
Group Classification ◽  
Nonlinear Filtration ◽  
Filtration Equation

Approximate symmetry analysis of nonlinear Rayleigh-wave equation

2018 ◽  
Vol 15 (04) ◽  
pp. 1850055
Author(s):  
Saeede Rashidi ◽  
S. Reza Hejazi ◽  
Elham Dastranj
Keyword(s):  
Wave Equation ◽  
Power Series ◽  
Small Parameter ◽  
Conservation Laws ◽  
Rayleigh Wave ◽  
Symmetry Analysis ◽  
Approximate Symmetry ◽  
Series Method ◽  
Power Series Method ◽  
New Exact Solutions

In this paper, the Lie approximate symmetry analysis is applied to investigate the new exact solutions of the Rayleigh-wave equation. The power series method is employed to solve some of the obtained reduced ordinary differential equations with a small parameter. We yield the new analytical solutions with small parameter which is effectively obtained by the proposed method. The concept of nonlinear self-adjointness is used to construct the conservation laws for Rayleigh-wave equation. It is shown that this equation is approximately nonlinearly self-adjoint and therefore desired conservation laws can be found using appropriate formal Lagrangians.

A basis of approximate conservation laws for PDEs with a small parameter

2006 ◽  
Vol 41 (6-7) ◽  
pp. 830-837 ◽  
Author(s):  
A.G. Johnpillai ◽  
A.H. Kara ◽  
F.M. Mahomed
Keyword(s):  
Small Parameter ◽  
Conservation Laws

scholarly journals Symmetry Group Classification and Conservation Laws of the Nonlinear Fractional Diffusion Equation with the Riesz Potential

Symmetry ◽  
2020 ◽  
Vol 12 (1) ◽  
pp. 178 ◽  
Author(s):  
Nikita S. Belevtsov ◽  
Stanislav Yu. Lukashchuk
Keyword(s):  
Diffusion Equation ◽  
Conservation Laws ◽  
Symmetry Group ◽  
Fractional Differential Equations ◽  
Riesz Potential ◽  
Fractional Diffusion ◽  
Group Classification ◽  
Fractional Diffusion Equation ◽  
Space Fractional Diffusion Equation ◽  
Fractional Differential

Symmetry properties of a nonlinear two-dimensional space-fractional diffusion equation with the Riesz potential of the order α ∈ ( 0 , 1 ) are studied. Lie point symmetry group classification of this equation is performed with respect to diffusivity function. To construct conservation laws for the considered equation, the concept of nonlinear self-adjointness is adopted to a certain class of space-fractional differential equations with the Riesz potential. It is proved that the equation in question is nonlinearly self-adjoint. An extension of Ibragimov’s constructive algorithm for finding conservation laws is proposed, and the corresponding Noether operators for fractional differential equations with the Riesz potential are presented in an explicit form. To illustrate the proposed approach, conservation laws for the considered nonlinear space-fractional diffusion equation are constructed by using its Lie point symmetries.

Group classification and conservation laws of anisotropic wave equations with a source

2016 ◽  
Vol 57 (8) ◽  
pp. 083504 ◽  
Author(s):  
N. H. Ibragimov ◽  
M. L. Gandarias ◽  
L. R. Galiakberova ◽  
M. S. Bruzon ◽  
E. D. Avdonina
Keyword(s):  
Conservation Laws ◽  
Wave Equations ◽  
Group Classification

scholarly journals Group Classification and Conservation Laws of a Class of Hyperbolic Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
J. C. Ndogmo
Keyword(s):  
Differential Equations ◽  
Conservation Laws ◽  
Linear Dependence ◽  
Hyperbolic Equations ◽  
Group Classification ◽  
The Family ◽  
The Given ◽  
Low Order

Abstracts. A method for the group classification of differential equations is proposed. It is based on the determination of all possible cases of linear dependence of certain indeterminates appearing in the determining equations of symmetries of the equation. The method is simple and systematic and applied to a family of hyperbolic equations. Moreover, as the given family contains several known equations with important physical applications, low-order conservation laws of some relevant equations from the family are computed, and the results obtained are discussed with regard to the symmetry integrability of a particular class from the underlying family of hyperbolic equations.

scholarly journals Finite dimensional dynamics for nonlinear filtration equation

2017 ◽  
Vol 112 ◽  
pp. 1361-1368
Author(s):  
Atlas V. Akhmetzyanov ◽  
Alexei G. Kushner ◽  
Valentin V. Lychagin
Keyword(s):  
Nonlinear Filtration ◽  
Filtration Equation ◽  
Finite Dimensional
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