A. Geyer and D.E. Pelinovsky
Spectral stability of periodic waves in the generalized reduced Ostrovsky equation
Lett Math Phys 107 (2017), 1293-1314
Abstract:
We consider stability of periodic travelling waves in the generalized reduced Ostrovsky
equation with respect to co-periodic perturbations. Compared to the recent
literature, we give a simple argument that proves spectral stability of all smooth periodic
travelling waves independently on the nonlinearity power. The argument is based
on the energy convexity and does not use coordinate transformations of the reduced
Ostrovsky equations to the semi-linear equations of the Klein-Gordon type.
Keywords:
Reduced Ostrovsky equation; periodic waves; spectral stability; negative index theory;