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It has taken me a long time to try and figure out what a system of coupled PDEs actually IS-and I still can't get a straight answer.

For example I have a system:

[itex]\dot{M}[/itex]=-L_{v}M

[itex]\dot{N}[/itex]=-L_{v+w}N

where here ,L, represents the lie derivative and M, N , v, w, are all elements of the sets of vector fields on a manifold. And I want to write this system as a pair of coupled PDEs with independent variables (x,t)[itex]\in[/itex]ℝxℝ.

I hope this question is clear and please answer sooner rather than later if you can.

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# Coupled PDE situation

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