GROUP CLASSIFICATION OF THREE-DIMENSIONAL VARIABLE-COEFFICIENT BURGERS EQUATION

2010 ◽  
Author(s):  
R. TRACINÀ ◽  
N. M. IVANOVA ◽  
C. SOPHOCLEOUS
Keyword(s):  
Variable Coefficient ◽  
Burgers Equation ◽  
Three Dimensional ◽  
Group Classification ◽  
Dimensional Variable

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.

Group Classification of Variable Coefficient $K\MakeLowercase{(m,n)}$ Equations

2014 ◽  
Author(s):  
Kyriakos Charalambous ◽  
Olena Vaneeva ◽  
Christodoulos Sophocleous
Keyword(s):  
Variable Coefficient ◽  
Group Classification

scholarly journals Group Classification Invariant Solutions of Burgers' Equation

2021 ◽  
pp. 19-32
Author(s):  
Mohammed Adam Abdualah Khatir ◽  
Mohammed Ali Basher ◽  
Blegiss Abdulaziz Abdulrahman Ebyed
Keyword(s):  
Mathematical Method ◽  
Wide Class ◽  
Burgers Equation ◽  
Algebraic Approach ◽  
Group Classification ◽  
Invariant Solutions ◽  
Smooth Functions ◽  
Preliminary Group

The aims of the present paper is to solve the problem of the group classification of the general Burgers’ equation u_t=f(x,u) u_x^2+g(x,u)u_xx, where f and g are arbitrary smooth functions of the variables x and u, by using Lie method. The paper is one of the few applications of an algebraic approach to the problem of group classification: We followed the analysis mathematical method using the method of preliminary group classification. A number of new interesting nonlinear invariant models which have nontrivial invariance algebras are obtained. The result of the work is a wide class of equations summarized in table form.

scholarly journals Lump and Lump-Type Solutions of the Generalized (3+1)-Dimensional Variable-Coefficient B-Type Kadomtsev-Petviashvili Equation

2019 ◽  
Vol 2019 ◽  
pp. 1-5 ◽  
Author(s):  
Yanni Zhang ◽  
Jing Pang
Keyword(s):  
Symbolic Computation ◽  
Bilinear Form ◽  
Variable Coefficient ◽  
Three Dimensional ◽  
Petviashvili Equation ◽  
Hirota Bilinear Form ◽  
Contour Plots ◽  
Dimensional Variable ◽  
Hirota Bilinear

Based on the Hirota bilinear form of the generalized (3+1)-dimensional variable-coefficient B-type Kadomtsev-Petviashvili equation, the lump and lump-type solutions are generated through symbolic computation, whose analyticity can be easily achieved by taking special choices of the involved parameters. The property of solutions is investigated and exhibited vividly by three-dimensional plots and contour plots.

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