Classical and nonclassical symmetries for Helmholtz Equation

[mathrock79]

" Classical and nonclassical symmetries for Helmholtz Equation " solitions help.
Thank you.

 

[HallsofIvy]

This makes no sense. Do you have a question about the Helmhotz equation?

 

[masudr]

It appears as if the OP got PhysicsForums and Google confused...

 

[mathrock79]

Dear HallsofIvy,
In general , how can I find symmetry groups in Helmholtz equation?

how can I pass from eq.2 to eq.3 by using the symmetry links?

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The classical symmetries groups for helmholtz equation wiht w² constant are given here for two-dimensional cartesian coordinates x and t.

For the equation Δ²u+w²u=0 (*****2) (U(x,t))

The generator of the symmetry grups Q is given by

Q=T(t,x,u)d/dt +X(t,x,u)d/du +U(t,x,u)d/du (d/dt and d/du partial turev)

With

T= a.x+b ,X=-a.t+c , U=d.u+q(x,t) (3*******)

Where q is any solution of eq.2**.

This last fact means that the Lie algebra for eq.2** is infinite-dimensonal with fundamental generators