Fixed points of a destabilized Kuramoto-Sivashinsky equation

We consider the family of destabilized Kuramoto-Sivashinsky equations in one spatial dimension u t + ? u x x x x + β u x x + γ u u x = α u for α, ? ? 0 and β , γ ? R . For certain parameter values, shock-like stationary solutions have been numerically observed. In this work we verify the existence of several such solutions using the framework of self-consistent bounds and validated numerics.

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