Travelling wave solutions for some two-component shallow water models

DOI10.1016/j.jde.2016.03.035zbMath1342.35247OpenAlexW2321785395MaRDI QIDQ281654

Denys Dutykh, Delia Ionescu-Kruse

Publication date: 11 May 2016

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2016.03.035

zbMATH Keywords

travelling wavessolitary wavesGreen-Naghdi modelCamassa-Holm equationscnoidal wavesphase-plane analysisSerre equations

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Solitary waves for incompressible inviscid fluids (76B25) Traveling wave solutions (35C07) Soliton solutions (35C08)

Related Items (10)

Bifurcations and exact traveling wave solutions for the regularized Schamel equation ⋮ On weakly singular and fully nonlinear travelling shallow capillary-gravity waves in the critical regime ⋮ Bifurcations and Exact Traveling Wave Solutions of the Celebrated Green–Naghdi Equations ⋮ Multisoliton solutions of the two-component Camassa–Holm system and their reductions ⋮ Multi-soliton solutions of a two-component Camassa–Holm system: Darboux transformation approach ⋮ Bifurcations and exact traveling wave solutions of a new two-component system ⋮ Dispersive Shallow Water Wave Modelling. Part II: Numerical Simulation on a Globally Flat Space ⋮ Completing the Study of Traveling Wave Solutions for Three Two-Component Shallow Water Wave Models ⋮ On the Cauchy problem for a periodic rotation-two-component μ-Hunter–Saxton system ⋮ On the geophysical Green-Naghdi system

Cites Work

• Unnamed Item
• Unnamed Item
• On an integrable two-component Camassa-Holm shallow water system
• Steady periodic flow induced by the Korteweg-de Vries equation
• On the development of the theory of the solitary wave. A historical essay
• The trajectories of particles in Stokes waves
• Efficient computation of steady solitary gravity waves
• The kinematics and stability of solitary and cnoidal wave solutions of the Serre equations
• Peakon-Antipeakon Interaction
• Variational derivation of two-component Camassa–Holm shallow water system
• Finite volume and pseudo-spectral schemes for the fully nonlinear 1D Serre equations
• Nonlinear Waves in Integrable and Nonintegrable Systems
• Interaction of "Solitons" in a Collisionless Plasma and the Recurrence of Initial States
• Nonlinear Water Waves with Applications to Wave-Current Interactions and Tsunamis
• Inverse scattering transform for the Degasperis–Procesi equation
• Inverse scattering transform for the Camassa–Holm equation
• The stability of solitary waves
• Symmetry of solitary waves
• A derivation of equations for wave propagation in water of variable depth
• A Modern Introduction to the Mathematical Theory of Water Waves
• An integrable shallow water equation with peaked solitons
• Korteweg-de Vries Equation and Generalizations. III. Derivation of the Korteweg-de Vries Equation and Burgers Equation
• Pressure beneath a Stokes wave
• A new two-component system modelling shallow-water waves
• The Korteweg-de Vries equation and water waves. Solutions of the equation. Part 1
• Variational Derivation of the Green–Naghdi Shallow-Water Equations
• Unsteady undular bores in fully nonlinear shallow-water theory

This page was built for publication: Travelling wave solutions for some two-component shallow water models