SOPDEs and Nonlinear Connections

The canonical k-tangent structure on $T^1_kQ=TQ\oplus\stackrel{k}…\oplus TQ$allowsustocharacterizenonlinearconnectionson$T^1_kQ$ and to develop G"unther’s (k-symplectic) Lagrangian formalism. We study the relationship between nonlinear connections and second-order partial differential equations (SOPDEs), which appear in G"unther’s Lagrangian formalism.