2009/10/15 by Matt Biesecker, Biesecker, Matt
Mathematics · #49N45 #53B50 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:49N45 #msc:53B50
paper · pdf · doi:10.48550/arxiv.0910.2933
arxiv created 2009/10/15 · arxiv updated 2009/12/01
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.