Conservation laws of scaling-invariant field equations

Physics – Mathematical Physics

Scientific paper

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18 pages, published version in J. Phys. A:Math. and Gen. (2003). Added discussion of vorticity conservation laws for fluid flo

Scientific paper

10.1088/0305-4470/36/32/305

A simple conservation law formula for field equations with a scaling symmetry is presented. The formula uses adjoint-symmetries of the given field equation and directly generates all local conservation laws for any conserved quantities having non-zero scaling weight. Applications to several soliton equations, fluid flow and nonlinear wave equations, Yang-Mills equations and the Einstein gravitational field equations are considered.

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