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Symmetry group classification for general Burgers’ equation

✍ Scribed by M. Nadjafikhah; R. Bakhshandeh-Chamazkoti

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
206 KB
Volume
15
Category
Article
ISSN
1007-5704

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✦ Synopsis

The present paper solves the problem of the group classification of the general Burgers' equation u t ¼ f ðx; uÞu 2

x þ gðx; uÞu xx , where f and g are arbitrary smooth functions of the variable 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 that is called preliminary group classification. Looking the adjoint representation of G E on its Lie algebra g 5 , we will deal with the construction of the optimal system of its one-dimensional subalgebras. The result of the work is a wide class of equations summarized in table form.

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Classification of Self Similar Solutions to a Generalized Burgers Equation
✍ E. Soewono; L. Debnath 📂 Article 📅 1994 🏛 Elsevier Science 🌐 English ⚖ 315 KB

A complete classification for the self-similar solutions to the generalized Burgers equation \[ u_{t}+u^{\beta} u_{x}=t^{N} u_{x x} \] of the form \(u(t, \eta)=A_{1} t^{-(1-N) / 2 \beta} F(\eta)\), where \(\eta=A_{2} x t^{-(1+N / 2}, A_{2}=1 / \sqrt{2 A}\), and \(A_{1}=\left(2 A_{2}\right)^{-1 / 6

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