On the stability of solitary waves for the Ostrovsky equation

DOI10.1090/S0033-569X-07-01065-8zbMath1144.35460MaRDI QIDQ5301292

Yue Liu

Publication date: 29 April 2008

Published in: Quarterly of Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

stabilitysolitary wavesOstrovsky equationweak rotation

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) KdV equations (Korteweg-de Vries equations) (35Q53) Solitary waves for incompressible inviscid fluids (76B25) Variational methods applied to problems in fluid mechanics (76M30) Continuation and prolongation of solutions to PDEs (35B60) Rotation in hydrodynamic stability (76E07)

Related Items

Conjugate gradient method for finding fundamental solitary waves ⋮ The Cauchy problem for quadratic and cubic Ostrovsky equation with negative dispersion ⋮ Well-posedness and dispersive/diffusive limit of a generalized Ostrovsky-Hunter equation ⋮ On the stability of solitary waves of a generalized Ostrovsky equation ⋮ Well-posedness of bounded solutions of the non-homogeneous initial-boundary value problem for the Ostrovsky–Hunter equation ⋮ Dispersive and diffusive limits for Ostrovsky-Hunter type equations ⋮ Stability of constrained solitary waves for the Ostrovsky-Vakhnenko model in the coastal zone ⋮ Periodic Traveling Waves of the Regularized Short Pulse and Ostrovsky Equations: Existence and Stability ⋮ On the solutions for an Ostrovsky type equation ⋮ Convergence of the Ostrovsky equation to the Ostrovsky-Hunter one ⋮ Oleinik type estimates for the Ostrovsky-Hunter equation ⋮ Well-posedness of the Ostrovsky-Hunter equation under the combined effects of dissipation and short-wave dispersion ⋮ Well‐posedness and unique continuation property for the generalized Ostrovsky equation with low regularity ⋮ The existence of ground states for fourth-order wave equations ⋮ Symmetry and uniqueness of the solitary-wave solution for the Ostrovsky equation ⋮ On the Cauchy Problem for the Ostrovsky Equation with Positive Dispersion ⋮ The Cauchy problem for the Ostrovsky equation with positive dispersion ⋮ Discontinuous Galerkin methods for the Ostrovsky-Vakhnenko equation ⋮ Solitary waves of a generalized Ostrovsky equation ⋮ Existence and stability of traveling waves of the fifth-order KdV equation ⋮ Well-posedness and weak rotation limit for the Ostrovsky equation ⋮ Some Wellposedness Results for the Ostrovsky–Hunter Equation

Cites Work

• Unnamed Item
• Unnamed Item
• On the lowest eigenvalue of the Laplacian for the intersection of two domains
• The concentration-compactness principle in the calculus of variations. The locally compact case. I
• Orbital stability of standing waves for some nonlinear Schrödinger equations
• Stability of Coulomb systems with magnetic fields. I: The one-electron atom
• On the existence of stationary solitary waves in a rotating fluid
• Solitary waves of generalized Kadomtsev-Petviashvili equations
• Cauchy problem for the Ostrovsky equation
• Stability of solitary waves and weak rotation limit for the Ostrovsky equation
• A Relation Between Pointwise Convergence of Functions and Convergence of Functionals
• Evolution Equations for Weakly Nonlinear, Long Internal Waves in a Rotating Fluid
• On the Surface Waves in a Shallow Channel with an Uneven Bottom
• Korteweg-de Vries Equation and Generalizations. II. Existence of Conservation Laws and Constants of Motion
• Approximate Analytical and Numerical Solutions of the Stationary Ostrovsky Equation