Asymptotic description of solitary wave trains in fully nonlinear shallow-water theory

DOI10.1016/j.physd.2008.03.031zbMath1155.35424arXiv0710.3379OpenAlexW2105382566MaRDI QIDQ947752

R. H. J. Grimshaw, Noel F. Smyth, Gennady A. El

Publication date: 7 October 2008

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0710.3379

zbMATH Keywords

undular boreshallow-water wavesWhitham theorysoliton train

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Solitary waves for incompressible inviscid fluids (76B25) Soliton equations (35Q51)

Related Items

Conservative discontinuous Galerkin methods for the nonlinear Serre equations ⋮ On periodic solutions of interfacial waves of finite amplitude ⋮ Error Estimates for Galerkin Approximations of the Serre Equations ⋮ Motion of dispersive shock edges in nonlinear pulse evolution ⋮ A SOLUTION OF THE CONSERVATION LAW FORM OF THE SERRE EQUATIONS ⋮ On the Galerkin/finite-element method for the Serre equations ⋮ Transcritical shallow-water flow past topography: finite-amplitude theory ⋮ Dispersive shock waves and modulation theory ⋮ Mechanical balance laws for fully nonlinear and weakly dispersive water waves ⋮ Transcritical flow over two obstacles: forced Korteweg–de Vries framework ⋮ A self-adaptive moving mesh method for the Camassa-Holm equation ⋮ Critical control in transcritical shallow-water flow over two obstacles ⋮ Solitary wave fission of a large disturbance in a viscous fluid conduit ⋮ Numerical solution of the fully non-linear weakly dispersive Serre equations for steep gradient flows ⋮ Theory of quasi-simple dispersive shock waves and number of solitons evolved from a nonlinear pulse ⋮ Transcritical flow over obstacles and holes: forced Korteweg–de Vries framework

Cites Work

• Asymptotic soliton train solutions of Kaup --- Boussinesq equations
• Undular bore transition in bi-directional conservative wave dynamics
• Slowly varying solitary waves. I. Korteweg-de Vries equation
• Resolution of a shock in hyperbolic systems modified by weak dispersion
• Evolution equations for strongly nonlinear internal waves
• Multiphase averaging and the inverse spectral solution of the Korteweg—de Vries equation
• A derivation of equations for wave propagation in water of variable depth
• Camassa–Holm, Korteweg–de Vries and related models for water waves
• Korteweg-de Vries Equation and Generalizations. III. Derivation of the Korteweg-de Vries Equation and Burgers Equation
• Fully nonlinear internal waves in a two-fluid system
• Non-linear dispersive waves
• A perturbation method for nonlinear dispersive wave problems
• Generation of undular bores in the shelves of slowly-varying solitary waves
• Unsteady undular bores in fully nonlinear shallow-water theory
• Generalized vorticity for bubbly liquid and dispersive shallow water equations
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item