Stability of constrained solitary waves for the Ostrovsky–Vakhnenko model in the coastal zone

Chen, Jianqing; Gao, Yuetian; Han, Fangyu

doi:10.1016/j.physd.2023.134028

Physica D: Nonlinear Phenomena

2024

DOI: 10.1016/j.physd.2023.134028

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Stability of constrained solitary waves for the Ostrovsky–Vakhnenko model in the coastal zone

Jianqing Chen,

Yuetian Gao,

Fangyu Han

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2024

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Cited by 2 publications

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Spectral Stability of Constrained Solitary Waves for the Generalized Singular Perturbed KdV Equation

Han,

Gao

2024

J Geom Anal

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Spectral Stability of Constrained Solitary Waves for the Generalized Singular Perturbed KdV Equation

Han,

Gao

2024

J Geom Anal

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Spectral stability of constrained solitary waves for a generalized Ostrovsky equation

Han,

Gao

2024

Proceedings of the Royal Society of Edinburgh: Section A Mathem

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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.

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Stability of constrained solitary waves for the Ostrovsky–Vakhnenko model in the coastal zone

Cited by 2 publications

References 30 publications

Spectral Stability of Constrained Solitary Waves for the Generalized Singular Perturbed KdV Equation

Spectral Stability of Constrained Solitary Waves for the Generalized Singular Perturbed KdV Equation

Spectral stability of constrained solitary waves for a generalized Ostrovsky equation

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