Higher-order Boussinesq equations for two-way propagation of shallow water waves
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Publication:860040
DOI10.1016/j.euromechflu.2006.02.003zbMath1171.76332OpenAlexW2163318888MaRDI QIDQ860040
Publication date: 22 January 2007
Published in: European Journal of Mechanics. B. Fluids (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.euromechflu.2006.02.003
Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Asymptotic methods, singular perturbations applied to problems in fluid mechanics (76M45) Solitary waves for incompressible inviscid fluids (76B25)
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Cites Work
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- A class of model equations for bi-directional propagation of capillary-gravity waves
- Weakly non-local solitons for capillary-gravity waves: Fifth-degree Korteweg-de Vries equation
- Existence of perturbed solitary wave solutions to a model equation for water waves
- Structural stability of the Korteweg-de Vries solitons under a singular perturbation
- Short-wave instabilities and ill-posed initial value problems
- A theory of solitary water-waves in the presence of surface tension
- A numerical study of an ill-posed Boussinesq equation arising in water and nonlinear lattices: Filtering and regularization techniques
- Some useful filtering techniques for illposed problems
- Exact traveling-wave solutions to bidirectional wave equations
- Analytical and numerical studies of a singularly perturbed Boussinesq equation.
- Boussinesq equations and other systems for small-amplitude long waves in nonlinear dispersive media. I: Derivation and linear theory
- A Boussinesq system for two-way propagation of nonlinear dispersive waves
- Solitary and periodic gravity—capillary waves of finite amplitude
- Hamiltonian perturbation theory and water waves
- Existence of solitary waves for water-wave models
- Existence and Nonexistence of Solitary Wave Solutions to Higher-Order Model Evolution Equations
- Weakly Nonlocal Solitary Waves in a Singularly Perturbed Korteweg–De Vries Equation
- A Modern Introduction to the Mathematical Theory of Water Waves
- The Generation and Evolution of Lump Solitary Waves in Surface-Tension-Dominated Flows
- A Formulation for Water Waves over Topography
- On Short‐Scale Oscillatory Tails of Long‐Wave Disturbances
- Exact N-soliton solutions of the wave equation of long waves in shallow-water and in nonlinear lattices
