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detools::detSys -- determining system for Lie point symmetries

Introduction

detools::detSys sets up the determining system for the generators of Lie point symmetries of a given system of differential equations. As for most methods in the detools library there exist several possibilities for entering the differential equations. The precise working of the method can be controlled by a number of options; especially it is possible to prescribe a special ansatz for the symmetry generators.

Call(s)

detools::detSys(de, indl, depl <, Ansatz = ans, Param = paraml> <, Expr = ebool> <, Interactive = bool> <, Autoreduced = bool>)
detools::detSys(df <, Ansatz = ans, Param = paraml> <, Expr = ebool> <, Interactive = bool> <, Autoreduced= bool>)

Parameters

de - the differential equation(s): either an expression or a list of expressions.
indl - the independent variable(s): a list of (indexed) identifiers.
depl - the dependent variable(s): a list of (indexed) identifiers.
df - the differential equation(s): either an element of a domain DF in Cat::DifferentialFunction or a list of such elements.

Options

Ansatz - prescribes an ansatz for the generators.
Param - lists the names of the parameters (functions or constants) contained in the ansatz.
Expr - determines the type of the output of detools::detSys.
Interactive - controls the behaviour, if detools::detSys has problems with solving the differential equations for their leading derivatives.
Autoreduced - controls whether the equations of the determining system are automatically simplified (autoreduced) by detools::detSys. If bool=FALSE, no simplifications are performed.

Returns

The determining system is returned as a list. The type of the list elements is controlled by the option Expr.

Side Effects

detools::detSys reads and writes some entries of the table detools::data. This includes especially further information about the used domains.

Related Functions

detools::ncDetSys

Details

Option: Ansatz=ans

Option: Param=paraml

Option: Expr=ebool

Option: Interactive=bool

Example 1

We compute the determining system for the heat equation diff(u(t,x),t)-diff(u(t,x),x,x)=0.

>> detools::detSys(u([t])-u([x,x]),[t,x],[u])
      [2 XI1([u]), 2 XI1([x]), XI2([u, u]), XI1([u, u]),
      
         2 XI2([x, u]) - PHI1([u, u]), 2 XI2([u]) + 2 XI1([x, u]),
      
         XI2([x, x]) - XI2([t]) - 2 PHI1([x, u]),
      
         2 XI2([x]) - XI1([t]) + XI1([x, x]),
      
         PHI1([t]) - PHI1([x, x])]

The output is a linear system of nine differential equations. The unknown functions XI1, XI2 and PHI1 represent the coefficients of the t-, x- and u-component of the symmetry generator, resp.

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