  The Ostrovskyi (Ostrovskyi-Vakhnenko/short pulse) equations are ubiquitous
models in mathematical physics. They describe water waves under the action of a
Coriolis force as well as the amplitude of a "short" pulse in an optical fiber.
In this paper, we rigorously construct ground traveling waves for these models
as minimizers of the Hamiltonian functional for any fixed $L^2$ norm. The
existence argument proceeds via the method of compensated compactness, but it
requires surprisingly detailed Fourier analysis arguments to rule out the
non-vanishing of the limits of the minimizing sequences. We show that all of
these waves are weakly non-degenerate and spectrally stable.
