ClassicalSymmetries

 ClassicalSymmetries[eq] gives the classical symmetries (point, generalized and conditional) for a differential equation or a system of differential equations.
• The result is a list {{{symmetry1, ...}, caseAssumptions}...} where each symmetryi is represented by an infinitesimal generator and, possible, by a set of constraints and caseAssumptions, the assumptions on the parameters of the system for the specific set of symmetries.
• The following options can be given :
 Verbose False whether to explicitly show each step taken for solving the system Hint {} explicitly specify the substitutions of the equations that will be used Conditional False whether to find the conditional symmetries instead ComplexDomain False whether to regard the uknown functions as complex Jetspace 0 whether to find the generalized symmetries of specific order KnownFunctions {} list any functions that will be considered as known SimplifyDeterminingEqs True whether to simplify the determining equations before solving them LogFile False whether to log the procedure Assumptions {} assumptions to make about the parameters ShowReport True whether to show the result to a seperate notebook
• For the purpose of substitutions when an equation has on the left hand side only one differential term this will be chosen for substitution. Otherwise the substitutions will be chosen automatically depending the equation or the system. With option Hint this automatic choice can be overidden.
• A seperate notepad is created when different cases arises. This can be suppresed with the option ShowReport.
Lie point symmetries of a non linear ODE. Here, substituting y" is chosen from the way the equation is given:
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Lie point symmetries of the KdV equation, here the substitution is chosen automatically:
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Lie point symmetries of an ODE including a parameter:
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The last case is the most general

Lie point symmetries of a system of ODES:
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In this case, the symmetries have been categorized by the value of the parameter M. The last case is the most general.

For this equation, its Lie point symmetries include also free functions restricted by differential constraint:
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Here, the third case is the most general.

Lie point symmetries of a system of PDEs that include integro-differential constraints.
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 Options   (6)