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- Publisher
- Springer Journals
- Copyright
- Copyright © 2012 by Springer Basel
- Subject
- Mathematics; Mathematical Methods in Physics; Analysis
- ISSN
- 1664-2368
- eISSN
- 1664-235X
- DOI
- 10.1007/s13324-012-0044-3
- Publisher site
- See Article on Publisher Site
Abstract
We consider the stability of ground state solitary waves of the generalized Ostrovsky equation $$( u_t - \beta u_{xxx} + f(u)_x)_x = \gamma u$$ , with homogeneous nonlinearities of the form $$f(u)=a_e|u|^p+a_o|u|^{p-1}u$$ . We obtain bounds on the function $$d$$ whose convexity determines the stability of the solitary waves. These bounds imply that, when $$2\le p<5$$ and $$a_o<0$$ , solitary waves are stable for $$c$$ near $$c_*=2\sqrt{\beta \gamma }$$ . These bounds also imply that, for $$\gamma >0$$ small, solitary waves are stable when $$2\le p<5$$ and unstable when $$p>5$$ . We also numerically compute the function $$d$$ , and thereby determine precise regions of stability and instability, for several nonlinearities.
Journal
Analysis and Mathematical Physics – Springer Journals
Published: Nov 5, 2012