Physical Review Letters · 1997 · 257 citations · 3 references
Natural SciencesMathematicsPhysicsDifferential EquationsDynamical SystemsMathematical PhysicsDissipative SystemsLagrangian DynamicsLagrangian MechanicsPartial Differential EquationsSystems Of Differential EquationsVariational FormulationConservation LawsDissipative Dynamical SystemsLagrange's EquationsLagrangian FormulationLagrangian SystemsNoether TheoremNoether's Theorem In MechanicsTransport Equations
This Letter presents an algorithm to obtain all local conservation laws for any system of field equations. The algorithm uses a formula which directly generates the conservation laws and does not depend on the system having a Lagrangian formulation, in contrast to Noether's theorem which requires a Lagrangian. Several examples are considered including dissipative systems inherently having no Lagrangian.
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