Year: 2024
Type: article
Abstract: We consider the existence and stability of constrained solitary wave solutions to the generalized Ostrovsky equation \begin{align*} \partial_x\left(\partial_t u+ \alpha\partial_x u+\partial_x(f(u))+\beta \partial_x^3u\right)=\gamma u,\quad \|u\|_{L^2}^2=\lambda \gt 0, \end{align*} where the homogeneous nonlinearities $f(s)=\alpha_0|s|^p+\alpha_1|s|^{p-1}s$ , with p > 1. If $\alpha_0,\alpha_1 \gt 0$ , $\alpha\in\mathbb{R}$ , and γ < 0 satisfying $\beta\gamma=-1$ , we show that for $1 \lt p \lt 5$ , there exists a constrained ground state traveling wave solution with travelling velocity $\omega \gt \alpha-2$ . Furthermore, we obtain the exponential decay estimates and the weak non-degeneracy of the solution. Finally, we show that the solution is spectrally stable. This is a continuation of recent work [1] on existence and stability for a water wave model with non-homogeneous nonlinearities.
DOI: 10.1017/prm.2024.86
Authors: Fangyu Han, Yuetian Gao
Institutions: Peking University, Fujian Normal University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
Awards: G3883852733, G6986954136
OpenAlex ID: W4404829136