scholarly journals New results on group classification of nonlinear diffusion–convection equations

2004 ◽  
Vol 37 (30) ◽  
pp. 7547-7565 ◽  
Author(s):  
Roman O Popovych ◽  
Nataliya M Ivanova
Keyword(s):  
Nonlinear Diffusion ◽  
Group Classification ◽  
Diffusion Convection

Perturbed invariant subspaces and approximate generalized functional variable separation solution for nonlinear diffusion–convection equations with weak source

2018 ◽  
Vol 32 (07) ◽  
pp. 1850093
Author(s):  
Ya-Rong Xia ◽  
Shun-Li Zhang ◽  
Xiang-Peng Xin
Keyword(s):  
Nonlinear Diffusion ◽  
Invariant Subspaces ◽  
Complete Classification ◽  
Variable Separation ◽  
Weak Source ◽  
Convection Equation ◽  
Functional Variable ◽  
Diffusion Convection

In this paper, we propose the concept of the perturbed invariant subspaces (PISs), and study the approximate generalized functional variable separation solution for the nonlinear diffusion–convection equation with weak source by the approximate generalized conditional symmetries (AGCSs) related to the PISs. Complete classification of the perturbed equations which admit the approximate generalized functional separable solutions (AGFSSs) is obtained. As a consequence, some AGFSSs to the resulting equations are explicitly constructed by way of examples.

scholarly journals Enhanced group classification of nonlinear diffusion–reaction equations with gradient-dependent diffusivity

2020 ◽  
Vol 484 (1) ◽  
pp. 123739 ◽  
Author(s):  
Stanislav Opanasenko ◽  
Vyacheslav Boyko ◽  
Roman O. Popovych
Keyword(s):  
Nonlinear Diffusion ◽  
Group Classification ◽  
Diffusion Reaction ◽  
Reaction Equations

Exact transient solutions to nonlinear diffusion-convection equations in higher dimensions

1994 ◽  
Vol 27 (16) ◽  
pp. 5455-5465 ◽  
Author(s):  
M P Edwards ◽  
P Broadbridge
Keyword(s):  
Nonlinear Diffusion ◽  
Higher Dimensions ◽  
Transient Solutions ◽  
Diffusion Convection

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
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