Global conservative and multipeakon conservative solutions for the modified Camassa-Holm system with coupling effects
type: Item
instance of: scholarly article
title: Global conservative and multipeakon conservative solutions for the modified Camassa-Holm system with coupling effects
zbMATH Open document ID: 1407.35181
DOI: 10.1155/2014/606249
author: Huabin Wen
author: Yujuan Wang
author: Hamid Reza Karimi
author: Yongduan Song
published in: Mathematical Problems in Engineering
publication date: 2019-02-08T00:00:00Z
review text: Summary: This paper investigates the continuation of solutions to the modified coupled two-component Camassa-Holm system after wave breaking. The underlying problem is rather challenging due to the mutual coupling effect between two components in the system. By introducing a novel transformation that makes use of a skillfully defined characteristic and a set of newly defined variables, the original system is converted into a Lagrangian equivalent system, from which the global conservative solution is obtained, which further allows for the establishment of the multipeakon conservative solution of the system. The results obtained herein are deemed useful for understanding the inevitable phenomenon near wave breaking.
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 35Q51
Mathematics Subject Classification ID: 76B15
Mathematics Subject Classification ID: 35B60
Mathematics Subject Classification ID: 35M31
zbMATH DE Number: 7016842
Wikidata QID: Q59066481
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/606249
OpenAlex ID: W2014592225
cites work: Well-posedness and blow-up solution for a modified two-component periodic Camassa-Holm system with peakons
cites work: Well posedness and blow-up solution for a new coupled Camassa–Holm equations with peakons
cites work: The Hamiltonian structure of the Camassa-Holm equation
cites work: An integrable shallow water equation with peaked solitons
cites work: On the scattering problem for the Camassa-Holm equation
cites work: The hydrodynamical relevance of the Camassa-Holm and Degasperis-Procesi equations
cites work: Wave breaking for nonlinear nonlocal shallow water equations
cites work: Special issue on the occasion of the 50th volume
cites work: Global conservative solutions of the Camassa-Holm equation
cites work: Global Conservative Solutions of the Camassa–Holm Equation—A Lagrangian Point of View
cites work: Periodic conservative solutions of the Camassa-Holm equation
cites work: GLOBAL CONSERVATIVE MULTIPEAKON SOLUTIONS OF THE CAMASSA–HOLM EQUATION
cites work: GLOBAL DISSIPATIVE SOLUTIONS OF THE CAMASSA–HOLM EQUATION
cites work: Global conservative and dissipative solutions of a coupled Camassa-Holm equations
cites work: On the global existence of dissipative solutions for the modified coupled Camassa-Holm system
cites work: On the multipeakon dissipative behavior of the modified coupled Camassa-Holm model for shallow water system
description: scientific article; zbMATH DE number 7016842