scholarly journals Geometric Flows of Curves, Two-Component Camassa-Holm Equation and Generalized Heisenberg Ferromagnet Equation

2021 ◽  
Vol 2090 (1) ◽  
pp. 012068
Author(s):  
Gulgassyl Nugmanova ◽  
Aigul Taishiyeva ◽  
Ratbay Myrzakulov ◽  
Tolkynai Myrzakul
Keyword(s):  
Heisenberg Ferromagnet ◽  
Geometric Flows ◽  
Space Curves ◽  
Holm Equation ◽  
Two Component

Abstract In this paper, we study the generalized Heisenberg ferromagnet equation, namely, the M-CVI equation. This equation is integrable. The integrable motion of the space curves induced by the M-CVI equation is presented. Using this result, the Lakshmanan (geometrical) equivalence between the M-CVI equation and the two-component Camassa-Holm equation is established.

scholarly journals On the Blow-Up of Solutions of a Weakly Dissipative Modified Two-Component Periodic Camassa-Holm System

2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
Yongsheng Mi ◽  
Chunlai Mu ◽  
Weian Tao
Keyword(s):  
Cauchy Problem ◽  
Blow Up ◽  
Strong Solutions ◽  
Well Posedness ◽  
Holm Equation ◽  
Two Component ◽  
The Cauchy Problem ◽  
Blow Up Rate

We study the Cauchy problem of a weakly dissipative modified two-component periodic Camassa-Holm equation. We first establish the local well-posedness result. Then we derive the precise blow-up scenario and the blow-up rate for strong solutions to the system. Finally, we present two blow-up results for strong solutions to the system.

On the weak solutions for the rotation-two-component Camassa–Holm equation

2020 ◽  
Vol 61 (6) ◽  
pp. 061514
Author(s):  
Li Yang ◽  
Chunlai Mu ◽  
Shouming Zhou ◽  
Xinyu Tu
Keyword(s):  
Weak Solutions ◽  
Holm Equation ◽  
Two Component

Wave breaking phenomenon for a modified two-component Dullin-Gottwald-Holm equation

2014 ◽  
Vol 55 (9) ◽  
pp. 093101 ◽  
Author(s):  
Panpan Zhai ◽  
Zhengguang Guo ◽  
Weiming Wang
Keyword(s):  
Wave Breaking ◽  
Holm Equation ◽  
Two Component

On Solutions to a Two-Component Generalized Camassa-Holm Equation

2010 ◽  
Vol 124 (3) ◽  
pp. 307-322 ◽  
Author(s):  
Zhengguang Guo ◽  
Yong Zhou
Keyword(s):  
Holm Equation ◽  
Two Component

scholarly journals Two-component generalizations of the Camassa–Holm equation

Nonlinearity ◽  
2017 ◽  
Vol 30 (2) ◽  
pp. 622-658 ◽  
Author(s):  
Andrew N W Hone ◽  
Vladimir Novikov ◽  
Jing Ping Wang
Keyword(s):  
Holm Equation ◽  
Two Component

scholarly journals Global Conservative Solutions of the Two-Component μ -Hunter–Saxton System

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Xiayang Shi ◽  
Jingjing Liu ◽  
Hongyang Zhang
Keyword(s):  
Holm Equation ◽  
Two Component

In this paper, we establish global conservative solutions of the two-component μ -Hunter–Saxton system by the methods developed in “A. Bressan, A. Constantin, Global Conservative Solutions of the Camassa-Holm Equation, Arch. Ration. Mech. Anal. 183 (2), 215–239 (2007)” and “H. Holden, X. Raynaud, Periodic Conservative Solutions of the Camassa-Holm Equation, Ann. Inst. Fourier (Grenoble) 58(3), 945–988 (2008).”

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