Possible New Recursion?

I’m still thinking about these conservation laws and finding a systematic method that doesn’t rely on identifying underlying symmetries in the problem.

More specifically, I’m trying to recreate the conservation laws from Olver without using the symmetry arguments directly.  After many sign errors, I can now create all of the conservation laws.  Unfortunately, it’s not a systematic process and relies on many clever insights.

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Constant Vorticity (Update)

In the quest to understand what happens to the stability as the strength of the vorticity increases, it’s important to predict precisely where the first instability will arise (in terms of the Floquet parameter \mu.

animation
Intersecting lines of opposite signature could give rise to a potential instability.  The two black dots follow the first to collisions; both of which yield instabilities for non-trivial solutions.

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