Qualitative analysis for a two-component peakon system with cubic nonlinearity

Shaojie Yang, Zhijun Qiao

Type: Article

Publication Date: 2022-12-01

Citations: 0

DOI: https://doi.org/10.1063/5.0123524

Abstract

This paper is devoted to studying a two-component peakon system with cubic nonlinearity, which is a two-component extension of the cubic Camassa–Holm equation. We first discuss the local well-posedness for the Cauchy problem of the system. Then, in light of a fine structure of the system, we present the precise blow-up scenario for strong solutions to the system and derive a new blow-up result with respect to initial data. Finally, peakon solutions are discussed as well.

Locations

Journal of Mathematical Physics - View - PDF

Similar Works

Action	Title	Year	Authors
+ PDF Chat	Blow-up phenomena for an integrable two-component Camassa–Holm system with cubic nonlinearity and peakon solutions	2015	Kai Yan Zhijun Qiao Yufeng Zhang
+	Blow-up phenomena for an integrable two-component Camassa-Holm system with cubic nonlinearity and peakon solutions	2015	Kai Yan Zhijun Qiao Yufeng Zhang
+ PDF Chat	On the blow up solutions to a two-component cubic Camassa-Holm system with peakons	2020	Kai Yan
+ PDF Chat	On a new two-component $b$-family peakon system with cubic nonlinearity	2018	Kai Yan Zhijun Qiao Yufeng Zhang
+	Blow-up for an integrable two-component Camassa-Holm system with cubic nonlinearity and peakon solutions	2022	Yongsheng Mi Daiwen Huang
+	Blow‐up of solutions for an integrable periodic two‐component Camassa‐Holm system with cubic nonlinearity	2022	Min Zhu Ying Wang
+	Blow-up scenario for a generalized Camassa–Holm equation with both quadratic and cubic nonlinearity	2019	Xiaofang Dong
+	Blow-up phenomena and peakons for the b-family of FORQ/MCH equations	2018	Shaojie Yang Zhijun Qiao Tianzhou Xu
+	On the Cauchy problem for a generalized Camassa-Holm equation with both quadratic and cubic nonlinearity	2013	Xingxing Liu Zhijun Qiao Zhaoyang Yin
+	WELL-POSEDNESS AND BLOWUP PHENOMENA FOR A THREE-COMPONENT CAMASSA–HOLM SYSTEM WITH PEAKONS	2012	Qiaoyi Hu Liyun Lin Ji Duo Jin
+	Blow-up phenomena and local well-posedness for a generalized Camassa–Holm equation with cubic nonlinearity	2016	Min Li Zhaoyang Yin
+	On the Cauchy problem for a generalized Camassa-Holm equation with both quadratic and cubic nonlinearity	2013	Xingxing Liu Zhijun Qiao Zhaoyang Yin
+	A three-component Camassa-Holm system with cubic nonlinearity and peakons	2013	Baoqiang Xia Ruguang Zhou Zhijun Qiao
+	Global existence of weak solutions for a three-component Camassa–Holm system with N-peakon solutions	2016	Wei Luo Zhaoyang Yin
+ PDF Chat	On the well-posedness of the Cauchy problem for the two-component peakon system in $C^k\cap W^{k,1}$	2024	Kenneth H. Karlsen Rybalko Ya
+ PDF Chat	A three-component Camassa-Holm system with cubic nonlinearity and peakons	2014	Baoqiang Xia Ruguang Zhou Zhijun Qiao
+	Qualitative analysis for the new shallow-water model with cubic nonlinearity	2020	Yongsheng Mi Yue Liu Daiwen Huang Boling Guo
+	Global existence and local well-posedness for a three-component Camassa–Holm system with N-peakon solutions	2015	Wei Luo Zhaoyang Yin
+	Global weak solutions for a three-component Camassa-Holm system with N-peakon solutions	2015	Wei Luo Zhaoyang Yin
+	Blow-up criteria for a two-component Camassa–Holm type system with cubic nonlinearity	2024	Bingqi Li Wenguang Cheng

Works That Cite This (0)

Action	Title	Year	Authors

Works Cited by This (36)

Action	Title	Year	Authors
+	Symplectic structures, their Bäcklund transformations and hereditary symmetries	1981	Benno Fuchssteiner A. S. Fokas
+	A note on well-posedness for Camassa–Holm equation	2003	Raphaël Danchin
+ PDF Chat	GLOBAL DISSIPATIVE SOLUTIONS OF THE CAMASSA–HOLM EQUATION	2006	Alberto Bressan Adrian Constantin
+	The Cauchy problem for an integrable two-component model with peakon solutions	2013	Yongsheng Mi Chunlai Mu
+ PDF Chat	A new integrable equation with cuspons and W/M-shape-peaks solitons	2006	Zhijun Qiao
+ PDF Chat	Global Conservative Solutions of the Camassa–Holm Equation	2006	Alberto Bressan Adrian Constantin
+	On the scattering problem for the Camassa-Holm equation	2001	Adrian Constantin
+ PDF Chat	A new integrable two-component system with cubic nonlinearity	2011	Junfeng Song Changzheng Qu Zhijun Qiao
+ PDF Chat	New integrable hierarchy, its parametric solutions, cuspons, one-peak solitons, and M/W-shape peak solitons	2007	Zhijun Qiao
+	The Camassa-Holm Hierarchy, N -Dimensional Integrable Systems, and Algebro-Geometric Solution on a Symplectic Submanifold	2003	Zhijun Qiao