Darboux transformation and Hamiltonian structure for the Jaulent–Miodek hierarchy

Autor:	Wen-Bao Ai, Bo Tian, Yan Jiang, Yu-Shan Xue
Rok vydání:	2012
Předmět:	Algebra Computational Mathematics Nonlinear Sciences::Exactly Solvable and Integrable Systems Transformation (function) Integrable system Hierarchy (mathematics) Hamiltonian structure Applied Mathematics Mathematical analysis Nonlinear evolution Symbolic computation Mathematics
Zdroj:	Applied Mathematics and Computation. 218:11738-11750
ISSN:	0096-3003
DOI:	10.1016/j.amc.2012.04.072
Popis:	Starting from the Jaulent–Miodek spectral problem, we derive the associated hierarchy of nonlinear evolution equations in this paper. It is shown that this hierarchy is completely integrable in the Liouville sense and possesses the Hamiltonian structure. Moreover, by virtue of symbolic computation, two types of Darboux transformations for the whole hierarchy are explicitly constructed, which enables us to find the new soliton-like, shock and anti-shock solutions for the Jaulent–Miodek hierarchy. Figures are presented to discuss the properties of the new soliton-like solutions.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::8ad3d4e1a216e766a272bd981f3ade21 https://doi.org/10.1016/j.amc.2012.04.072 Zobrazit plný text záznamu Full Text from ScienceDirect