I PDEs greater than order 2 with real world applications?

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Came across this today, a fourth order PDE - the Kuramoto–Sivashinsky equation, apparently used to model flames

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https://en.wikipedia.org/wiki/Kuramoto–Sivashinsky_equation

Any other examples of high order PDEs with actual applications?

amoto%E2%80%93Sivashinsky_spatiotemporal_evolution.png
 
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Another example is one dimensional transverse waves on a uniform slender beam, which satisfy ## u_{xxxx} + a^2 \, u_{tt} = 0 ##. This is a special case of the Euler-Bernoulli equation
https://en.wikipedia.org/wiki/Euler–Bernoulli_beam_theory
 
Thread 'Direction Fields and Isoclines'
I sketched the isoclines for $$ m=-1,0,1,2 $$. Since both $$ \frac{dy}{dx} $$ and $$ D_{y} \frac{dy}{dx} $$ are continuous on the square region R defined by $$ -4\leq x \leq 4, -4 \leq y \leq 4 $$ the existence and uniqueness theorem guarantees that if we pick a point in the interior that lies on an isocline there will be a unique differentiable function (solution) passing through that point. I understand that a solution exists but I unsure how to actually sketch it. For example, consider a...

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