A review: The symmetry of the one-dimensional Burgers equation

We present the relation between the one-dimensional Burgers equation with the Lie group by applying the prolongation method. The Burgers equation itself is a kind of nonlinear wave equation that generally represents the nonlinear diffusion and can also create both solitary wave solution and multisol...

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Bibliographic Details
Main Author: Prayitno, Teguh Budi
Format: Conference Proceeding
Language:English
Subjects:
Burgers equation
Generators
Group theory
Lie groups
Linear equations
Multiplication
Operators (mathematics)
Prolongation
Solitary waves
Wave equations
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Summary:We present the relation between the one-dimensional Burgers equation with the Lie group by applying the prolongation method. The Burgers equation itself is a kind of nonlinear wave equation that generally represents the nonlinear diffusion and can also create both solitary wave solution and multisoliton solution. To use the method, we consider the theorem than can prolong the definition of the partial derivative. The above method produces some generators of its group and by applying the multiplication table it can be shown that the group forms the Lie algebra. We obtain that two generators are the operator of energy and the operator of linear momentum.
ISSN:0094-243X
1551-7616
DOI:10.1063/1.5132671