Comparisons between model equations for long waves

DOI10.1007/BF01238818zbMath0791.35123MaRDI QIDQ1322802

Jerry L. Bona, John P. Albert

Publication date: 18 July 1994

Published in: Journal of Nonlinear Science (Search for Journal in Brave)

zbMATH Keywords

dispersion relationsKorteweg-de Vries equationslong wave modelsregularized long-wave equations

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15)

Related Items

Comparison between model equations for long waves and blow-up phenomena, Derivation and comparison of model equations for interfacial capillary-gravity waves in deep water, Numerical computation of solitary wave solutions of the Rosenau equation, Comparison between Boussinesq‐ and Whitham–Boussinesq‐type systems, The regularized Benjamin-Ono and BBM equations: well-posedness and nonlinear stability, Solitary-wave solutions of Benjamin-Ono and other systems for internal waves. I: Approximations, SPATIAL ANALYTICITY PROPERTIES OF NONLINEAR WAVES, The Cauchy problem for the Rosenau equation, Exact traveling waves solutions for long waves and blow-up phenomena, Orbital stability of negative solitary waves, The effect of dissipation on solutions of the generalized Korteweg-de Vries equation, Error analysis of a spectral projection of the Benjamin-Ono equation, Long wave approximations for water waves, The Cauchy problem and stability of solitary-wave solutions for RLW--KP-type equations, Well-posedness and ill-posedness results for the regularized Benjamin-Ono equation in weighted Sobolev spaces, Existence and stability of solitary-wave solutions of equations of Benjamin-Bona-Mahony type.

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Dispersive blowup of solutions of generalized Korteweg-de Vries equations
• The Korteweg-de Vries equation in a quarter plane, continuous dependence results
• Nonlocal models for nonlinear, dispersive waves
• An initial- and boundary-value problem for a model equation for propagation of long waves
• Sur quelques généralisations de l'équation de Korteweg-de Vries
• Nonlinear wave motion in magnetoelasticity
• The Korteweg–de Vries Equation, Posed in a Quarter-Plane
• Convergence of Galerkin Approximations for the Korteweg-de Vries Equation
• Fully discrete galerkin methods for the korteweg-de vries equation
• On Some High-Order Accurate Fully Discrete Galerkin Methods for the Korteweg-de Vries Equation
• A Conservative Finite Element Method for the Korteweg-de Vries Equation
• A note on limiting cases of sobolev embeddings and convolution inequalities
• A Superconvergent Finite Element Method for the Korteweg-de Vries Equation
• An evaluation of a model equation for water waves
• The Korteweg-de Vries equation and water waves. Part 2. Comparison with experiments
• Conservative, high-order numerical schemes for the generalized Korteweg—de Vries equation
• A note on tsunamis: their generation and propagation in an ocean of uniform depth
• Internal waves of permanent form in fluids of great depth
• Model equations for long waves in nonlinear dispersive systems