Boundary value problems for Boussinesq type systems

DOI10.1007/s11040-004-1650-6zbMath1070.35030OpenAlexW2051689409MaRDI QIDQ1781139

Beatrice Pelloni, Athanassios S. Fokas

Publication date: 16 June 2005

Published in: Mathematical Physics, Analysis and Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11040-004-1650-6

zbMATH Keywords

Boussinesq systemspectral transformKdV-KdV systemtwo-way propagation of water waves

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Integral representations of solutions to PDEs (35C15)

Related Items

Evolution PDEs and augmented eigenfunctions. half-line ⋮ Fokas’s Unified Transform Method for linear systems ⋮ A dispersive model for undular bores ⋮ Integral representations for the double-diffusivity system on the half-line ⋮ Wave breaking in Boussinesq models for undular bores ⋮ Numerical solution of the `classical' Boussinesq system ⋮ The Unified Transform and the Water Wave Problem ⋮ Error estimates for Galerkin approximations of the “classical” Boussinesq system ⋮ Asymptotic nonlinear and dispersive pulsatile flow in elastic vessels with cylindrical symmetry ⋮ Finite volume schemes for dispersive wave propagation and runup ⋮ Mechanical balance laws for Boussinesq models of surface water waves ⋮ Fokas diagonalization of piecewise constant coefficient linear differential operators on finite intervals and networks ⋮ Temporal boundary value problems in interfacial fluid dynamics ⋮ A regularized shallow-water waves system with slip-wall boundary conditions in a basin: theory and numerical analysis ⋮ Extended water wave systems of Boussinesq equations on a finite interval: theory and numerical analysis

Cites Work

• Unnamed Item
• Unnamed Item
• Regularity and uniqueness of solutions to the Boussinesq system of equations
• Existence of solutions for the Boussinesq system of equations
• Integrable nonlinear evolution equations on the half-line
• Boussinesq equations and other systems for small-amplitude long waves in nonlinear dispersive media. I: Derivation and linear theory
• On the integrability of linear and nonlinear partial differential equations
• Integrable evolution equations in time-dependent domains
• Two–dimensional linear partial differential equations in a convex polygon
• The Fundamental Differential Form and Boundary-Value Problems
• The nonlinear Schrödinger equation on the interval
• A unified transform method for solving linear and certain nonlinear PDEs
• A new transform method for evolution partial differential equations
• Well-posed boundary value problems for linear evolution equations on a finite interval
• Integral transforms, spectral representation and the d-bar problem
• A transform method for linear evolution PDEs on a finite interval
• Numerical modelling of two-way propagation of nonlinear dispersive waves
• An initial-boundary value problem for the Korteweg-de Vries equation posed on a finite interval