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Review of Symbolic Software for Lie Symmetry Analysis
 CRC HANDBOOK OF LIE GROUP ANALYSIS OF DIFFERENTIAL EQUATIONS, VOLUME 3: NEW TRENDS IN THEORETICAL DEVELOPMENT AND COMPUTATIONAL METHODS, CHAPTER 13
, 1995
"... Computer algebra packages and tools that aid in the computation of Lie symmetries of differential equations are reviewed. The methods and algorithms of Lie symmetry analysis are brifley outlined. Examples illustrate the use of the symbolic software. ..."
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Computer algebra packages and tools that aid in the computation of Lie symmetries of differential equations are reviewed. The methods and algorithms of Lie symmetry analysis are brifley outlined. Examples illustrate the use of the symbolic software.
The Computer Algebra Package CRACK for Investigating PDEs
, 1997
"... Contents 1 The purpose of CRACK 2 2 How to apply CRACK 4 2.1 The call . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2 The result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.3 Flags . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..."
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Cited by 28 (11 self)
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Contents 1 The purpose of CRACK 2 2 How to apply CRACK 4 2.1 The call . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2 The result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.3 Flags . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.4 Help . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 3 Contents of the CRACK package 6 3.1 Decoupling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 3.2 Integrating exact PDEs . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3.3 Direct separation of PDEs . . . . . . . . . . . . . . . . . . . . . . . . 11 3.4 Indirect separation of PDEs . . . . . . . . . . . . . . . . . . . . . . . 12 3.5 Solving standard ODEs . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1 4 Examples 14 4.1 Investigating symmetries of ODEs/PDEs and systems o
Symmetry group analysis of the shallow water and semigeostrophic
"... The twodimensional shallow water equations and their semigeostrophic approximation that arise in meteorology and oceanography are analysed from the point of view of symmetry groups theory. A complete classification of their associated classical symmetries, potential symmetries, variational symmetr ..."
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Cited by 8 (0 self)
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The twodimensional shallow water equations and their semigeostrophic approximation that arise in meteorology and oceanography are analysed from the point of view of symmetry groups theory. A complete classification of their associated classical symmetries, potential symmetries, variational symmetries and conservation laws is found. The semigeostrophic equations are found to lack conservation of angular momentum. We also show how the particle relabelling symmetry can be used to rewrite the semigeostrophic equations in such a way that a welldefined formal series solution, smooth only in time, may be carried out. We show that such solutions are in the form of an ‘infinite linear cascade’. 1.
Partial and Complete Linearization of PDEs Based on Conservation Laws
 in “Trends in Mathematics: Differential Equations with Symbolic Computation
, 2005
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, 2008
"... The integration of systems of linear PDEs using conservation laws of syzygies ..."
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The integration of systems of linear PDEs using conservation laws of syzygies
The computer algebra package Crack for solving overdetermined systems of equations
, 2004
"... 1.1 Help to help................................ 2 1.2 Help to inspect data........................... 2 1.3 Help to proceed.............................. 3 ..."
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1.1 Help to help................................ 2 1.2 Help to inspect data........................... 2 1.3 Help to proceed.............................. 3
Symbolic software for Lie group analysis
 IN THEORETICAL DEVELOPMENTS AND COMPUTATIONAL METHODS. CHAPTER 13
, 1994
"... A survey of techniques and symbolic programs for the determination of Lie symmetry groups of systems of differential equations is presented. The purpose, methods and algorithms of symmetry analysis are outlined. An exhaustive review of the literature, including old and modern books and papers presen ..."
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A survey of techniques and symbolic programs for the determination of Lie symmetry groups of systems of differential equations is presented. The purpose, methods and algorithms of symmetry analysis are outlined. An exhaustive review of the literature, including old and modern books and papers presenting key concepts is given. Special attention is paid to methods for reducing the determining equations into standard form, and their subsequent integration. Several examples illustrate the use of the Lie symmetry software. Throughout the paper, new trends in the development of symbolic packages for Lie symmetry analysis are indicated.