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Partial differential equations (PDEs): Existence and uniqueness, regularity, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDEs, conservation laws, qualitative dynamics.
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Flow of evolutionary vector fields
Consider a smooth vector bundle $\pi: E\rightarrow M$, the associated infinite jet bundle $J^\infty(\pi)$, and evolutionary vector fields $\partial_\varphi = \sum_{i,\sigma}(D_\sigma\varphi^i)\frac{\p …
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Flow of evolutionary vector fields
I believe I have found the answer. I think it works like this, but I still have to verify it. In case of any other people that might have the same question, I will outline it here. It relies on the fo …