Abstract
The stability of the peaked periodic wave 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 L 2 norm of co-periodic perturbations to the peaked periodic wave, from which it follows that the peaked periodic wave is linearly unstable. We also prove that the peaked periodic wave with a parabolic profile is the unique peaked wave in the space of periodic L 2 functions with zero mean and a single minimum per period.
Original language | English |
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Pages (from-to) | 1188-1208 |
Number of pages | 21 |
Journal | SIAM Journal on Mathematical Analysis |
Volume | 51 |
Issue number | 2 |
DOIs | |
Publication status | Published - 2019 |
Keywords
- Characteristics
- Instability
- Peaked periodic wave
- Reduced Ostrovsky equation
- Semigroup