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.

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

scholarly journals Group Classification of a General Bond-Option Pricing Equation of Mathematical Finance

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Tanki Motsepa ◽  
Chaudry Masood Khalique ◽  
Motlatsi Molati
Keyword(s):  
Option Pricing ◽  
Three Dimensional ◽  
Mathematical Finance ◽  
Group Classification ◽  
Lie Point Symmetries ◽  
Group Invariant ◽  
Black Scholes ◽  
Group Invariant Solutions ◽  
Bond Option

We carry out group classification of a general bond-option pricing equation. We show that the equation admits a three-dimensional equivalence Lie algebra. We also show that some of the values of the constants which result from group classification give us well-known models in mathematics of finance such as Black-Scholes, Vasicek, and Cox-Ingersoll-Ross. For all such values of these arbitrary constants we obtain Lie point symmetries. Symmetry reductions are then obtained and group invariant solutions are constructed for some cases.

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 Abductive Networks For Two-Group Classification: A Comparison With Neural Networks

2011 ◽  
Vol 15 (2) ◽  
pp. 1 ◽  
Author(s):  
Anurag Agarwal
Keyword(s):  
Neural Networks ◽  
Linear Mapping ◽  
Group Classification ◽  
Type Ii ◽  
Artificial Intelligence Technique ◽  
Empirical Tests ◽  
Multivariate Discriminant ◽  
Better Than

<span>In this study, a new Artificial Intelligence technique for non-linear mapping called Abductive Networks is used for two-group classification of firms. The results are compared with Neural Networks, another AI technique, which has been shown to perform better than the traditional statistical techniques such as multivariate discriminant analysis and logit. In empirical tests, Abductive Networks perform as well or better than Neural Networks on various criteria of measurement such as Type 1 / Type II accuracy criteria and Distance Between Centroids.</span>

scholarly journals Algebraic Method for Group Classification of (1+1)-Dimensional Linear Schrödinger Equations

2018 ◽  
Vol 157 (1) ◽  
pp. 171-203 ◽  
Author(s):  
Célestin Kurujyibwami ◽  
Peter Basarab-Horwath ◽  
Roman O. Popovych
Keyword(s):  
Algebraic Method ◽  
Group Classification ◽  
Schrodinger Equations ◽  
Schrödinger Equations
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