A. Geyer and D.E. Pelinovsky
Linear instability and uniqueness of the peaked periodic wave in the reduced Ostrovsky equation
SIAM Journal of Mathematical Analysis 51, 1188-1208 (2019)
Abstract:
Stability of the peaked periodic waves in the reduced Ostrovsky equation has remained
an open problem for a long time. In order to solve this problem we obtain sharp bounds
on the exponential growth of the L2 norm of co-periodic perturbations to the peaked periodic
wave, from which it follows that the peaked periodic wave is orbitally unstable. We also prove that the
peaked periodic wave with a parabolic profile is the unique peaked wave in the space of periodic L2
functions with zero mean and a single minimum per period.
Keywords:
Reduced Ostrovsky equation; peaked periodic waves; linear instability; method of characteristics;