Mathematics – Differential Geometry
Scientific paper
2009-10-15
Mathematics
Differential Geometry
Scientific paper
A complete solution to the multiplier version of the inverse problem of the calculus of variations is given for a class of hyperbolic systems of second-order partial differential equations in two independent variables. The necessary and sufficient algebraic and differential conditions for the existence of a variational multiplier are derived. It is shown that the number of independent variational multipliers is determined by the nullity of a completely algebraic system of equations associated to the given system of partial differential equations. An algorithm for solving the inverse problem is demonstrated on several examples. Systems of second-order partial differential equations in two independent and dependent variables are studied and systems which have more than one variational formulation are classified up to contact equivalence.
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