Fixed points of a destabilized Kuramoto–Sivashinsky equation

We consider the family of destabilized Kuramoto–Sivashinsky equations in one spatial dimension ut+νuxxxx+βuxx+γuux=αuut+νuxxxx+βuxx+γuux=αu for α, ν   ≥ 0 and β,γ∈Rβ,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.