TY - JOUR

T1 - Spectral stability of periodic waves in the generalized reduced Ostrovsky equation

AU - Geyer, Anna

AU - Pelinovsky, Dmitry

PY - 2017/2/2

Y1 - 2017/2/2

N2 - 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 independent of 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.

AB - 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 independent of 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.

KW - Energy-to-period map

KW - Negative index theory

KW - Reduced Ostrovsky equations

KW - Stability of periodic waves

UR - http://resolver.tudelft.nl/uuid:ad387b5a-8c0f-446f-9e61-04f49c929567

UR - http://www.scopus.com/inward/record.url?scp=85011620548&partnerID=8YFLogxK

U2 - 10.1007/s11005-017-0941-3

DO - 10.1007/s11005-017-0941-3

M3 - Article

AN - SCOPUS:85011620548

VL - 107

SP - 1293

EP - 1314

JO - Letters in Mathematical Physics

JF - Letters in Mathematical Physics

SN - 0377-9017

IS - 7

ER -