Numerical solution of KdV-KdV systems of Boussinesq equations. I: The numerical scheme and generalized solitary waves
From MaRDI portal
Publication:871087
DOI10.1016/j.matcom.2006.10.004zbMath1158.35410OpenAlexW2081451815MaRDI QIDQ871087
Jerry L. Bona, Dimitrios Mitsotakis, Vassilios A. Dougalis
Publication date: 15 March 2007
Published in: Mathematics and Computers in Simulation (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.matcom.2006.10.004
KdV equations (Korteweg-de Vries equations) (35Q53) Solitary waves for incompressible inviscid fluids (76B25) Finite element methods applied to problems in fluid mechanics (76M10)
Related Items
Finite element methods for a system of dispersive equations ⋮ Local discontinuous Galerkin methods for the \(abcd\) nonlinear Boussinesq system ⋮ Conservation Laws for a Generalized Coupled Boussinesq System of KdV–KdV Type ⋮ An ADER-type scheme for a class of equations arising from the water-wave theory ⋮ A numerical scheme for an improved Green-Naghdi model in the Camassa-Holm regime for the propagation of internal waves ⋮ Exponential B-splines for numerical solutions to some Boussinesq systems for water waves ⋮ Structure-preserving reduced-order modeling of Korteweg-de Vries equation ⋮ A dispersive model for undular bores ⋮ Norm-inflation results for purely BBM-type Boussinesq systems ⋮ Mass and spring dimer Fermi–Pasta–Ulam–Tsingou nanopterons with exponentially small, nonvanishing ripples ⋮ Numerical solution of the `classical' Boussinesq system ⋮ On the multi-symplectic structure of Boussinesq-type systems. I: Derivation and mathematical properties ⋮ The design of conservative finite element discretisations for the vectorial modified KdV equation ⋮ Petviashvili type methods for traveling wave computations. II: Acceleration with vector extrapolation methods ⋮ A Boussinesq system for two-way propagation of interfacial waves ⋮ Error estimates for Galerkin approximations of the “classical” Boussinesq system ⋮ Stability of solitary-wave solutions of systems of dispersive equations ⋮ Finite volume schemes for dispersive wave propagation and runup ⋮ Numerical solution of Boussinesq systems of the Bona-Smith family ⋮ Mechanical balance laws for Boussinesq models of surface water waves ⋮ Uniform stabilization of numerical schemes for the critical generalized Korteweg-de Vries equation with damping ⋮ Error estimates for a fully discrete spectral scheme for nonlinear Boussinesq systems ⋮ On solitary-wave solutions of Boussinesq/Boussinesq systems for internal waves ⋮ On time relaxed schemes and formulations for dispersive wave equations ⋮ Stability analysis for a fully discrete spectral scheme for Boussinesq systems ⋮ A regularized shallow-water waves system with slip-wall boundary conditions in a basin: theory and numerical analysis
Cites Work
- Unnamed Item
- A class of model equations for bi-directional propagation of capillary-gravity waves
- Numerical solution of Boussinesq systems of the Bona-Smith family
- Exact traveling-wave solutions to bidirectional wave equations
- Oscillatory integrals and phenomena beyond all algebraic orders with applications to homoclinic orbits in reversible systems
- Solitary waves of a coupled Korteweg-de Vries system
- 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
- Long wave approximations for water waves
- Numerical study of generalized interfacial solitary waves
- Non–existence of truly solitary waves in water with small surface tension
- Weakly nonlocal gravity–capillary solitary waves
- Boussinesq equations and other systems for small-amplitude long waves in nonlinear dispersive media: II. The nonlinear theory
- Conservative, high-order numerical schemes for the generalized Korteweg—de Vries equation
