Periodic Traveling Waves of the Regularized Short Pulse and Ostrovsky Equations: Existence and Stability
From MaRDI portal
Publication:2967919
DOI10.1137/15M1037901zbMath1361.35038OpenAlexW2594036597MaRDI QIDQ2967919
Milena Stanislavova, Sevdzhan A. Hakkaev, Atanas G. Stefanov
Publication date: 9 March 2017
Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1137/15m1037901
Asymptotic behavior of solutions to PDEs (35B40) Stability in context of PDEs (35B35) KdV equations (Korteweg-de Vries equations) (35Q53) Periodic solutions to PDEs (35B10) Boundary value problems for nonlinear higher-order PDEs (35G30) Traveling wave solutions (35C07)
Related Items (9)
High-frequency instabilities of the Ostrovsky equation ⋮ Periodic multi-pulses and spectral stability in Hamiltonian PDEs with symmetry ⋮ Spectral stability of periodic waves in the generalized reduced Ostrovsky equation ⋮ Hybrid analysis and modeling, eclecticism, and multifidelity computing toward digital twin revolution ⋮ Existence, regularity and symmetry of periodic traveling waves for Gardner-Ostrovsky type equations ⋮ Spectral instability of the peaked periodic wave in the reduced Ostrovsky equations ⋮ Linear Instability and Uniqueness of the Peaked Periodic Wave in the Reduced Ostrovsky Equation ⋮ Waves of maximal height for a class of nonlocal equations with homogeneous symbols ⋮ Bäcklund transformation and nonlinear superposition formula for the two-component short pulse equation
Cites Work
- Unnamed Item
- Unnamed Item
- Global existence of small-norm solutions in the reduced Ostrovsky equation
- Well-posedness and small data scattering for the generalized Ostrovsky equation
- On stationary solutions of the reduced Ostrovsky equation: periodic waves, compactons and compound solitons
- Existence of multi-pulses of the regularized short-pulse and Ostrovsky equations
- Wave breaking in the short-pulse equation
- Stability of cnoidal waves
- The modulational instability for a generalized Korteweg-de Vries equation
- Geometric theory of semilinear parabolic equations
- The calculation of multi-soliton solutions of the Vakhnenko equation by the inverse scattering method.
- Propagation of ultra-short optical pulses in cubic nonlinear media
- Spectral and dynamical stability of nonlinear waves
- Stability and weak rotation limit of solitary waves of the Ostrovsky equation
- Explicit solutions of the reduced Ostrovsky equation
- On the Spectral and Orbital Stability of Spatially Periodic Stationary Solutions of Generalized Korteweg-de Vries Equations
- Wave Breaking in the Ostrovsky–Hunter Equation
- An index theorem for the stability of periodic travelling waves of Korteweg–de Vries type
- Stability of Solitary Waves of a Generalized Ostrovsky Equation
- Solitons in a nonlinear model medium
- The two loop soliton solution of the Vakhnenko equation
- The stability of solutions of Vakhnenko's equation
- The Reduced Ostrovsky Equation: Integrability and Breaking
- Solitary Waves of the Regularized Short Pulse and Ostrovsky Equations
- Count of eigenvalues in the generalized eigenvalue problem
- On the stability of solitary waves for the Ostrovsky equation
- Stability of solitary waves for the Ostrovsky equation
- Stability of periodic travelling shallow-water waves determined by Newton's equation
- Solitary wave solutions of the short pulse equation
- Lieb–Thirring estimates for non-self-adjoint Schrödinger operators
- Ostrovsky and Hunter's generic wave equation for weakly dispersive waves: matched asymptotic and pseudospectral study of the paraboloidal travelling waves (corner and near-corner waves)
- Counting eigenvalues via the Krein signature in infinite-dimensional Hamiltonian systems
This page was built for publication: Periodic Traveling Waves of the Regularized Short Pulse and Ostrovsky Equations: Existence and Stability
