Lie symmetry analysis and exact explicit solutions for general Burgers' equation
Hanze Liu,Jibin Li,Quanxin Zhang +2 more
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TLDR
In this article, the Lie symmetry analysis is performed for the general Burgers' equation and the exact solutions and similarity reductions generated from the symmetry transformations are provided, some new method and techniques are employed simultaneously.About:
This article is published in Journal of Computational and Applied Mathematics.The article was published on 2009-06-01 and is currently open access. It has received 104 citations till now. The article focuses on the topics: Burgers' equation & Lie group.read more
Citations
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Lie symmetry analysis and exact solutions for the short pulse equation
TL;DR: In this paper, the Lie symmetry analysis and the generalized symmetry method are performed for a short pulse equation (SPE), and the exact analytic solutions are obtained by using the power series method.
Journal ArticleDOI
On invariant analysis of some time fractional nonlinear systems of partial differential equations. I
Komal Singla,R. K. Gupta +1 more
TL;DR: In this paper, Lie point symmetries for systems of time fractional partial differential equations including Ito system, coupled Burgers equations, coupled Korteweg de Vries equations, Hirota-Satsuma coupled KdV equations, and coupled nonlinear Hirota equations have been obtained.
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A systematic literature review of Burgers’ equation with recent advances
TL;DR: The objectives of this paper are to discuss the recent developments in mathematical modelling of Burgers’ equation, and throw some light on the plethora of challenges which need to be overcome in the research areas and give motivation for the next breakthrough to take place in a numerical simulation of ordinary / partial differential equations.
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Lie symmetry analysis, optimal systems and exact solutions to the fifth-order KdV types of equations☆
TL;DR: In this paper, the Lie symmetry analysis is performed on the fifth-order KdV types of equations which arise in modeling many physical phenomena, and the similarity reductions and exact solutions are obtained based on the optimal system method.
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Symmetry reduction, exact solutions and conservation laws of a new fifth-order nonlinear integrable equation
TL;DR: By applying Lie symmetry method, the corresponding Lie algebra and similarity reductions of a new fifth-order nonlinear integrable equation are obtained and the conservation laws are given.
References
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Partial Differential Equations
TL;DR: In this paper, the authors present a theory for linear PDEs: Sobolev spaces Second-order elliptic equations Linear evolution equations, Hamilton-Jacobi equations and systems of conservation laws.
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Applications of Lie Groups to Differential Equations
TL;DR: In this paper, the Cauchy-Kovalevskaya Theorem has been used to define a set of invariant solutions for differential functions in a Lie Group.
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TL;DR: The real and complex number system as discussed by the authors is a real number system where the real number is defined by a real function and the complex number is represented by a complex field of functions.
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Method for solving the Korteweg-deVries equation
TL;DR: In this paper, a method for solving the initial value problem of the Korteweg-deVries equation is presented which is applicable to initial data that approach a constant sufficiently rapidly as