29 research outputs found
The algebraic hyperstructure of elementary particles in physical theory
Algebraic hyperstructures represent a natural extension of classical
algebraic structures. In a classical algebraic structure, the composition of
two elements is an element, while in an algebraic hyperstructure, the
composition of two elements is a set. Algebraic hyperstructure theory has a
multiplicity of applications to other disciplines. The main purpose of this
paper is to provide examples of hyperstructures associated with elementary
particles in physical theory.Comment: 13 page
Conservation laws for self-adjoint first order evolution equations
In this work we consider the problem on group classification and conservation
laws of the general first order evolution equations. We obtain the subclasses
of these general equations which are quasi-self-adjoint and self-adjoint. By
using the recent Ibragimov's Theorem on conservation laws, we establish the
conservation laws of the equations admiting self-adjoint equations. We
illustrate our results applying them to the inviscid Burgers' equation. In
particular an infinite number of new symmetries of these equations are found
and their corresponding conservation laws are established.Comment: This manuscript has been accepted for publication in Journal of
Nonlinear Mathematical Physic
A symmetry classification for a class of (2+1)-nonlinear wave equation
In this paper, a symmetry classification of a -nonlinear wave equation
where is a smooth function on , using
Lie group method, is given. The basic infinitesimal method for calculating
symmetry groups is presented, and used to determine the general symmetry group
of this -nonlinear wave equation
Symmetry group classification for general Burger's equation
The present paper solves the problem of the group classification of the
general Burgers' equation , where and are
arbitrary smooth functions of the variable and , by using Lie method.
The paper is one of the few applications of an algebraic approach to the
problem of group classification: 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.Comment: 9 page
Symmetry analysis of Black-Scholes equation for small values of volatility and rate of return
In this paper, we present approximate symmetries of the Black-Scholes equation for small values
of volatility and rate of return parameters. A novel method for obtaining the approximate symmetry of a singularly perturbed partial differential equation (PDE) is introduced. Further, we compute the optimal system in the singular case. Finally, by combining two methods, a new approach that calculates the approximate generators for admitted Lie groups of asset price is provided
Approximate Hamiltonian Symmetry Groups and Recursion Operators for Perturbed Evolution Equations
The method of approximate transformation groups, which was proposed by Baikov et al. (1988 and 1996), is extended on Hamiltonian and bi-Hamiltonian systems of evolution equations. Indeed, as a main consequence, this extended procedure is applied in order to compute the approximate conservation laws and approximate recursion operators corresponding to these types of equations. In particular, as an application, a comprehensive analysis of the problem of approximate conservation laws and approximate recursion operators associated to the Gardner equation with the small parameters is presented
Approximate Hamiltonian Symmetry Groups and Recursion Operators for Perturbed Evolution Equations
The method of approximate transformation groups, which was proposed b
SYMMETRY CLASSIFICATION OF NEWTONIAN INCOMPRESSIBLEFLUID’S EQUATIONS FLOW IN TURBULENT BOUNDARY LAYERS
Lie group method is applicable to both linear and non-linear partial differential equations, which leads to find new solutions for partial differential equations. Lie symmetry group method is applied to study Newtonian incompressible fluid’s equations flow in turbulent boundary layers. The symmetry group and its optimal system are given, and group invariant solutions associated to the symmetries are obtained. Finally the structure of the Lie algebra such as Levi decomposition, radical subalgebra, solvability and simplicity of symmetries is given