Jet Bundle - Partial Differential Equations

Partial Differential Equations

Let (E, π, M) be a fiber bundle. An r-th order partial differential equation on π is a closed embedded submanifold S of the jet manifold Jr(π). A solution is a local section σ ∈ ΓW(π) satisfying, forall p in M.

Let us consider an example of a first order partial differential equation.

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