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
SN - 0377-9017
VL - 107
SP - 1293
EP - 1314
JO - Letters in Mathematical Physics
JF - Letters in Mathematical Physics
IS - 7
ER -