Modulational instability in the Ostrovsky equation and related models (Q6642436)

This paper deals with the dispersive generalized Ostrovsky equation \N\[\N( u_t +\beta \mathcal{M} u_x +(u^2)_x\bigr)_x - \gamma u=0, \quad\gamma >0, \>\beta \in \mathbb{R}\setminus \{ 0\} ,\N\]\Nwhere \(\mathcal{M}\) is a Fourier multiplier operator\N\NThe authors study the modulational instability of small-amplitude periodic traveling wave solutions, investigate the invertibility of the associated linearized operator in the vicinity of the origin and derive a modulational instability index that depends on the dispersion and nonlinearity.