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ClassicalSymmetries

ClassicalSymmetries[eq]
gives the classical symmetries (point, generalized and conditional) for a differential equation or a system of differential equations.

MORE INFORMATION

To use ClassicalSymmetries, you first need to load the SYM Package using Needs["SYM`"].

The result is a list {{{symmetry₁, ...}, caseAssumptions}...} where each symmetry_i 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.

Basic Examples (6)

Lie point symmetries of a non linear ODE. Here, substituting y" is chosen from the way the equation is given:

Lie point symmetries of the KdV equation, here the substitution is chosen automatically:

Lie point symmetries of an ODE including a parameter:

The last case is the most general

Lie point symmetries of a system of ODES:

Click for copyable input

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:

Here, the third case is the most general.

Lie point symmetries of a system of PDEs that include integro-differential constraints.

DeterminingEqs SolveOverdeterminedEqs

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