Derivation of Generalized Camassa-Holm Equations from Boussinesq-type Equations

DOI10.1080/14029251.2016.1199493zbMath1420.35065arXiv1605.04549OpenAlexW2402880153MaRDI QIDQ5231029

H. A. Erbay, Saadet Erbay, Albert Kohen Erkip

Publication date: 29 August 2019

Published in: Journal of Nonlinear Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1605.04549

zbMATH Keywords

asymptotic expansionsgeneralized Camassa-Holm equationmodified Camassa-Holm equationimproved Boussinesq equationfractional Camassa-Holm equation

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Asymptotic expansions of solutions to PDEs (35C20) Solitary waves in solid mechanics (74J35)

Related Items (5)

The generalized fractional Benjamin-Bona-Mahony equation: analytical and numerical results ⋮ Decay of solitary waves of fractional Korteweg-de Vries type equations ⋮ The Cauchy problem for generalized fractional Camassa-Holm equation in Besov space ⋮ On the Cauchy problem for the fractional Camassa-Holm equation ⋮ On the stability of solitary wave solutions for a generalized fractional Benjamin–Bona–Mahony equation

Cites Work

• Unnamed Item
• The Camassa-Holm equation as the long-wave limit of the improved Boussinesq equation and of a class of nonlocal wave equations
• A note on solitary waves for modified forms of Camassa-Holm and Degasperis-Procesi equations
• The hydrodynamical relevance of the Camassa-Holm and Degasperis-Procesi equations
• Wave breaking for nonlinear nonlocal shallow water equations
• Some tricks from the symmetry-toolbox for nonlinear equations: Generalizations of the Camassa-Holm equation
• A selection of nonlinear problems in water waves, analysed by perturbation-parameter techniques
• Derivation of the Camassa-Holm equations for elastic waves
• On the scattering problem for the Camassa-Holm equation
• On the Blow-Up Scenario for the Generalized Camassa–Holm Equation
• Variational derivation of the Camassa-Holm shallow water equation
• Generalizations of the Camassa–Holm equation
• Stability and instability of solitary waves of Korteweg-de Vries type
• A shallow water equation on the circle
• Stability of peakons
• An integrable shallow water equation with peaked solitons
• Camassa–Holm, Korteweg–de Vries and related models for water waves
• A Variational Approach to the Stability of Periodic Peakons
• A Hamiltonian–Krein (Instability) Index Theory for Solitary Waves to KdV‐Like Eigenvalue Problems
• Model equations for long waves in nonlinear dispersive systems
• Global existence and blow-up for a class of nonlocal nonlinear Cauchy problems arising in elasticity
• On the Cauchy problem for the generalized Camassa-Holm equation

This page was built for publication: Derivation of Generalized Camassa-Holm Equations from Boussinesq-type Equations