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.
Highlights
The celebrated Camassa-Holm equation (CHE) has the form ut + κ ux − uxxt + 3uux = 2uxuxx + uuxxx, (1.1)where u = u(x, t) is the fluid velocity in the x direction and κ = const is related to the critical shallow water wave speed
The CHE shares most of the important properties of integrable equations like the N -soliton solutions, the bi-Hamiltonian structure, the Lax representation (LR) and so on
We have considered the M-CVI equation and the 2-CHE
Summary
The CHE shares most of the important properties of integrable equations like the N -soliton solutions, the bi-Hamiltonian structure, the Lax representation (LR) and so on. In the case, when κ = 0, the CHE (1.1) has the so-called peakon solutions. Several important generalizations of the CHE including integrable cases but many other (non-integrable or whose integrability has not been determined) have been discovered [1]-[29]. We study the 2-CHE, its relation with the geometry of space curves and the equivalent spin system.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
