Two-component generalizations of the Camassa–Holm equation. (9th January 2017)

• Record Type: Journal Article
• Authors: Hone, Andrew N W; Novikov, Vladimir; Wang, Jing Ping
• Is Part Of: Nonlinearity. Volume 30:Number 2(2017:Feb.)
• Page Start: 622
• Page End: 658
• Publication Date: 2017-01-09
• Subjects: Camassa–Holm-type equations -- perturbative symmetry approach -- bi-Hamiltonian systems -- reciprocal transformations; 37K10 -- 35G20; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/aa5490
• Languages: English
• ISSNs: 0951-7715

Abstract

Abstract: A classification of integrable two-component systems of non-evolutionary partial differential equations that are analogous to the Camassa–Holm equation is carried out via the perturbative symmetry approach. Independently, a classification of compatible pairs of Hamiltonian operators of specific forms is carried out, in order to obtain bi-Hamiltonian structures for the same systems of equations. Using reciprocal transformations, some exact solutions and Lax pairs are also constructed for the systems considered.