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LAVFSolve

find a LAVF object whose solution space is the sum of the solution spaces of given LAVF objects.

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

LAVFSolve( obj, output = out, consts = c)

Parameters

obj

-

a LAVF object that is of finite type (see IsFiniteType)

out

-

(optional) a string: either "solution", "basis", or "lavf"

c

-

(optional) a name or a list of names

Description

• 

The LAVFSolve method attempts to solve the determining system in a LAVF object.

• 

If solving is successful then by default the method returns a list of solution vector fields.

• 

The returned output can be as a basis (by specifying output = "basis") or a new LAVF object (by specifying output = "lavf").

• 

For a returned output that involves constants of integration variables, by default these variables are labeled as  _C1, _C2, ...

• 

The constant of integration variables can be renamed by specifying the optional argument consts = c.

– 

By specifying consts = alpha (i.e. a name), the constants of integration will be named as α1,α2,α3,..

– 

By specifying consts = [alpha, beta, phi...] (i.e. a list of names), the constants of integration will be named as α,β,φ,

• 

This is a front-end to the LHSolve method for solving the determining system. LHSolve is associated with the LHPDE object, see Overview of the LHPDE object for more detail.

• 

The method throws an exception if the LAVF is not of finite type.

• 

This method is associated with the LAVF object. For more detail, see Overview of the LAVF object.

Examples

with(LieAlgebrasOfVectorFields):

Typesetting:-Settings(userep=true):

Typesetting:-Suppress([xi(x,y),eta(x,y)]):

V := VectorField(xi(x,y)*D[x] + eta(x,y)*D[y], space = [x,y]);

Vξx+ηy

(1)

E2 := LHPDE([diff(xi(x,y),y,y)=0, diff(eta(x,y),x)=-diff(xi(x,y),y), diff(eta(x,y),y)=0, diff(xi(x,y),x)=0], indep = [x,y], dep = [xi, eta]);

E2ξy,y=0,ηx=ξy,ηy=0,ξx=0,indep=x,y,dep=ξ,η

(2)

Construct a vector fields system for E(2).

L := LAVF(V, E2);

Lξx+ηy&whereξy,y=0,ξx=0,ηx=ξy,ηy=0

(3)

LAVFSolve(L);

_C1y+_C3x+_C1x+_C2y

(4)

LAVFSolve(L, consts = [alpha, beta, delta]);

αy+δx+αx+βy

(5)

LAVFSolve(L, output = "basis");

yx+xy,y,x

(6)

LAVFSolve(L, output = "lavf", consts = alpha);

ξx+ηy&whereξ=yα1+α3,η=xα1+α2

(7)

Compatibility

• 

The LAVFSolve command was introduced in Maple 2020.

• 

For more information on Maple 2020 changes, see Updates in Maple 2020.

See Also

LieAlgebrasOfVectorFields (Package overview)

LAVF (Object overview)

LieAlgebrasOfVectorFields[VectorField]

LieAlgebrasOfVectorFields[LHPDE]

LieAlgebrasOfVectorFields[LAVF]

IsFiniteType

LHSolve