SymmetryAnalysis(JB1, xi, eta)

jet.spad line 5153 [edit on github]

• JB1 : JetBundleCategory
• xi : Union(Symbol, List(Symbol))
• eta : Union(Symbol, List(Symbol))

SymmetryAnalysis(JB, xi, eta) provides procedures for the symmetry analysis of differential equations over a given jet bundle. Currently there exist only some procedures to set up the determining system for the symmetry generators of Lie point symmetries.

ansatz : () -> JetVectorField(JB1, JetBundleExpression(JB1))

ansatz() returns a general ansatz for a symmetry generator.

detSys : (List(JetBundleExpression(JB1)), JetVectorField(JB1, JetBundleExpression(JB1))) -> List(JetBundleExpression(JB1))

detSys(sys, vf) computes the determining system for symmetry generators of the system sys with a given ansatz for the generators. It is assumed that each equation can be solved for its leading derivative.

detSys : (List(JetBundleExpression(JB1)), List(JB1), JetVectorField(JB1, JetBundleExpression(JB1))) -> List(JetBundleExpression(JB1))

detSys(sys, sjb, vf) computes the determining system for symmetry generators of the system sys with a given ansatz for the generators. sjb contains jet variables for which the individual equations can be solved.

detSys : List(JetBundleExpression(JB1)) -> List(JetBundleExpression(JetBundleSymAna(JB1, xi, eta)))

detSys(sys) computes the determining system for symmetry generators of the system sys. It is assumed that each equation can be solved for its leading derivative.

detSysNS : (List(JetBundleExpression(JB1)), JetVectorField(JB1, JetBundleExpression(JB1))) -> List(JetBundleExpression(JB1))

detSysNS(sys, vf) computes the determining system for symmetry generators without assuming solvability of the equations for some derivatives.

detSysNS : List(JetBundleExpression(JB1)) -> List(JetBundleExpression(JetBundleSymAna(JB1, xi, eta)))

detSysNS(sys, vf) computes the determining system for symmetry generators without assuming solvability of the equations for some derivatives.

linearize : List(JetBundleExpression(JetBundleSymAna(JB1, xi, eta))) -> List(JetBundleLinearFunction(JetBundleSymAna(JB1, xi, eta), JetBundleXExpression(JetBundleSymAna(JB1, xi, eta))))

linearize(sys) tries to retract all equations in sys to a linear one. If that is not possible, an error occurs.

ncDetSys : (List(JetBundleExpression(JB1)), JetVectorField(JB1, JetBundleExpression(JB1))) -> List(JetBundleExpression(JB1))

ncDetSys(sys, vf) computes the determining system for generators of conditional symmetries of sys with a given ansatz for the vector fields.

ncDetSys : (List(JetBundleExpression(JB1)), List(JB1), JetVectorField(JB1, JetBundleExpression(JB1))) -> List(JetBundleExpression(JB1))

ncDetSys(sys, sjb, vf) computes the determining system for generators of conditional symmetries of sys. The meaning of the further arguments is the same as in detSys.

ncDetSys : List(JetBundleExpression(JB1)) -> List(JetBundleExpression(JetBundleSymAna(JB1, xi, eta)))

ncDetSys(sys) computes the determining system for generators of conditional symmetries of sys. It makes the same assumptions as detSys.

transform : JetBundleExpression(JB1) -> JetBundleExpression(JetBundleSymAna(JB1, xi, eta))

transform(f) transforms expressions between the different function types involved.