scholarly journals Lie Group Classification of a Generalized Lane-Emden Type System in Two Dimensions

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Motlatsi Molati ◽  
Chaudry Masood Khalique
Keyword(s):  
Quadratic Forms ◽  
Type System ◽  
Lie Symmetry ◽  
Two Dimensions ◽  
Group Classification ◽  
Classical Approach ◽  
Physical Sciences ◽  
Lie Group Classification ◽  
Physical Phenomena

The aim of this work is to perform a complete Lie symmetry classification of a generalized Lane-Emden type system in two dimensions which models many physical phenomena in biological and physical sciences. The classical approach of group classification is employed for classification. We show that several cases arise in classifying the arbitrary parameters, the forms of which include amongst others the power law nonlinearity, and exponential and quadratic forms.

Lie Group Classification for a Generalised Coupled Lane-Emden System in Dimension One

2014 ◽  
Vol 4 (4) ◽  
pp. 301-311 ◽  
Author(s):  
Ben Muatjetjeja ◽  
Chaudry Masood Khalique
Keyword(s):  
Exact Solution ◽  
Lie Algebra ◽  
Lie Group ◽  
Group Classification ◽  
One Dimension ◽  
Dimension One ◽  
Lie Group Classification ◽  
Physical Phenomena

AbstractIn this article, we discuss the generalised coupled Lane-Emden system u” + H(v) = 0, v” + G(u) = 0 that applies to several physical phenomena. The Lie group classification of the underlying system shows that it admits a ten-dimensional equivalence Lie algebra. We also show that the principal Lie algebra in one dimension has several possible extensions, and obtain an exact solution for an interesting particular case via Noether integrals.

Lie group classification of the N-th-order nonlinear evolution equations

2011 ◽  
Vol 54 (12) ◽  
pp. 2553-2572 ◽  
Author(s):  
ShouFeng Shen ◽  
ChangZheng Qu ◽  
Qing Huang ◽  
YongYang Jin
Keyword(s):  
Lie Group ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Group Classification ◽  
Nonlinear Evolution Equations ◽  
Lie Group Classification

Lie group classification of second-order ordinary difference equations

2000 ◽  
Vol 41 (1) ◽  
pp. 480-504 ◽  
Author(s):  
Vladimir Dorodnitsyn ◽  
Roman Kozlov ◽  
Pavel Winternitz
Keyword(s):  
Lie Group ◽  
Difference Equations ◽  
Group Classification ◽  
Second Order ◽  
Lie Group Classification

scholarly journals Lie symmetries of generalized Kawahara equations

2020 ◽  
pp. 3-10
Author(s):  
O.O. Vaneeva ◽  
◽  
A.Yu. Zhalij ◽  
Keyword(s):  
Variable Coefficients ◽  
Lie Symmetry ◽  
Group Classification ◽  
Lie Symmetries

We carry out the group classification of a normalized class of generalized Kawahara equations with variable coefficients. Admissible transformations are studied, and the partition of the class into two normalized subclasses is performed. For each of these subclasses, the respective equivalence groupoids are found. As a result, all equations from the class admitting Lie symmetry extensions are revealed.

scholarly journals Lie group classification of first-order delay ordinary differential equations

2018 ◽  
Vol 51 (20) ◽  
pp. 205202 ◽  
Author(s):  
Vladimir A Dorodnitsyn ◽  
Roman Kozlov ◽  
Sergey V Meleshko ◽  
Pavel Winternitz
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Lie Group ◽  
Group Classification ◽  
First Order ◽  
Lie Group Classification

scholarly journals Lie Group Classification of Generalized Variable Coefficient Korteweg-de Vries Equation with Dual Power-Law Nonlinearities with Linear Damping and Dispersion in Quantum Field Theory

Symmetry ◽  
2022 ◽  
Vol 14 (1) ◽  
pp. 83
Author(s):  
Oke Davies Adeyemo ◽  
Chaudry Masood Khalique
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Power Law ◽  
Lie Group ◽  
Variable Coefficient ◽  
Variable Coefficients ◽  
Group Classification ◽  
Quantum Field ◽  
Lie Group Classification

Many physical phenomena in fields of studies such as optical fibre, solid-state physics, quantum field theory and so on are represented using nonlinear evolution equations with variable coefficients due to the fact that the majority of nonlinear conditions involve variable coefficients. In consequence, this article presents a complete Lie group analysis of a generalized variable coefficient damped wave equation in quantum field theory with time-dependent coefficients having dual power-law nonlinearities. Lie group classification of two distinct cases of the equation was performed to obtain its kernel algebra. Thereafter, symmetry reductions and invariant solutions of the equation were obtained. We also investigate various soliton solutions and their dynamical wave behaviours. Further, each class of general solutions found is invoked to construct conserved quantities for the equation with damping term via direct technique and homotopy formula. In addition, Noether’s theorem is engaged to furnish more conserved currents of the equation under some classifications.

scholarly journals Group Classification of a Generalized Lane-Emden System

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Ben Muatjetjeja ◽  
Chaudry Masood Khalique ◽  
Fazal Mahmood Mahomed
Keyword(s):  
Pattern Formation ◽  
Chemical Reactions ◽  
Group Classification ◽  
Population Evolution ◽  
Physical Phenomena

We perform the group classification of the generalized Lane-Emden systemxu′′+nu′+xHv=0,  xv′′+nv′+xgu=0, which occurs in many applications of physical phenomena such as pattern formation, population evolution, and chemical reactions. We obtain four cases depending on the values ofn.

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