Stability of Solitary Waves of a Generalized Ostrovsky Equation
نویسندگان
چکیده
Considered herein is the stability problem of solitary wave solutions of a generalized Ostrovsky equation, which is a modification of the Korteweg-de Vries equation widely used to describe the effect of rotation on surface and internal solitary waves or capillary waves.
منابع مشابه
On the Stability of Solitary Waves of a Generalized Ostrovsky Equation
We consider the stability of ground state solitary waves of the generalized Ostrovsky equation (ut − βuxxx + f(u)x)x = γu, with homogeneous nonlinearities of the form f(u) = ae|u| + ao|u|u. We obtain bounds on the function d whose convexity determines the stability of the solitary waves. These bounds imply that, when 2 ≤ p < 5 and ao < 0, solitary waves are stable for c near c∗ = 2 √ βγ. These ...
متن کاملStability and Weak Rotation Limit of Solitary Waves of the Ostrovsky Equation
In this paper we study several aspects of solitary wave solutions of the Ostrovsky equation. Using variational methods, we show that as the rotation parameter goes to zero, ground state solitary waves of the Ostrovsky equation converge to solitary waves of the Korteweg-deVries equation. We also investigate the properties of the function d(c) which determines the stability of the ground states. ...
متن کاملSpectral stability of periodic waves in the generalized reduced Ostrovsky equation
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 transformati...
متن کاملSolitary Waves, Shock Waves and Singular Solitons of the Generalized Ostrovsky-Benjamin-Bona-Mahoney Equation
This paper obtains the solitary wave, shock wave as well as singular soliton solutions to the generalized OstrovskyBenjamin-Bona-Mahoney (gO-BBM) equation. The ansatz method is applied to obtain the solutions. Several constraint conditions for the parameters are derived that establish the existence of the soliton solutions.
متن کاملOn strongly interacting internal waves in a rotating ocean and coupled Ostrovsky equations.
In the weakly nonlinear limit, oceanic internal solitary waves for a single linear long wave mode are described by the KdV equation, extended to the Ostrovsky equation in the presence of background rotation. In this paper we consider the scenario when two different linear long wave modes have nearly coincident phase speeds and show that the appropriate model is a system of two coupled Ostrovsky...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- SIAM J. Math. Analysis
دوره 38 شماره
صفحات -
تاریخ انتشار 2006