Existence and stability of solitary wave solutions of the Benjamin equation

DOI10.1006/jdeq.1998.3525zbMath0923.35151OpenAlexW2011310675MaRDI QIDQ1283888

Jaime Angulo Pava

Publication date: 31 August 1999

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jdeq.1998.3525

zbMATH Keywords

Lagrangian multiplierconcentration compactness methodvariational representationconstrained functionalnonlocal Benjamin-Ono equation

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) KdV equations (Korteweg-de Vries equations) (35Q53) Euler-Poisson-Darboux equations (35Q05)

Related Items (16)

Pointwise convergence problem of the Korteweg-de Vries-Benjamin-Ono equation ⋮ On a system of nonlinear Schrödinger equations with quadratic interaction and L2-critical growth ⋮ The well-posedness of the Korteweg-de Vries-Benjamin-Ono equation ⋮ On the propagation of regularity and decay of solutions to the Benjamin equation ⋮ Benjamin-Ono and Intermediate Long Wave Equations: Modeling, IST and PDE ⋮ Fractional derivative estimates in Gevrey spaces, global regularity and decay for solutions to semilinear equations in \(\mathbb R^n\) ⋮ Sharp well-posedness for the Benjamin equation ⋮ Global smoothing for the periodic Benjamin equation in low-regularity spaces ⋮ Analysis of Malmquist-Takenaka-Christov rational approximations with applications to the nonlinear Benjamin equation ⋮ Global well-posedness of the two-dimensional Benjamin equation in the energy space ⋮ On the controllability and stabilization of the linearized Benjamin equation on a periodic domain ⋮ A Sharp Bilinear Estimate for the Bourgain-Type Space with Application to the Benjamin Equation ⋮ On the controllability and stabilization of the Benjamin equation on a periodic domain ⋮ Nonlinear dispersive equations: classical and new frameworks ⋮ Local well-posedness for periodic Benjamin equation with small initial data ⋮ Existence and stability of solitary-wave solutions of equations of Benjamin-Bona-Mahony type.

Cites Work

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• Existence and asymptotic properties of solitary-wave solutions of Benjamin-type equations
• Lyapunov stability of ground states of nonlinear dispersive evolution equations
• Stability and instability of solitary waves of Korteweg-de Vries type
• Existence of solitary waves for water-wave models
• Positivity Properties and Stability of Solitary–Wave Solutions of Model Equations For Long Waves
• A new kind of solitary wave
• On the stability theory of solitary waves
• Model equations for waves in stratified fluids
• Solitary-Wave Solutions of the Benjamin Equation
• Solitary and periodic waves of a new kind
• COMMUTATORS OF SINGULAR INTEGRAL OPERATORS

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