Nonlinear Integrable Couplings of Levi Hierarchy and WKI Hierarchy-Reference-Cited by-同舟云学术

Nonlinear Integrable Couplings of Levi Hierarchy and WKI Hierarchy

Published:2014 Issue: Volume:2014 Page:1-7
ISSN:1085-3375
Container-title:Abstract and Applied Analysis
language:en
Short-container-title:Abstract and Applied Analysis

Author:

Shan Zhengduo¹²³⁴,Yang Hongwei⁵,Yin Baoshu¹⁴

Affiliation:

1. Institute of Oceanology, Chinese Academy of Sciences, Qingdao 266071, China

2. School of Mathematics and Physics, Qingdao University of Science and Technology, Qingdao 266061, China

3. Graduate School, University of Chinese Academy of Sciences, Beijing 100049, China

4. Key Laboratory of Ocean Circulation and Wave, Chinese Academy of Sciences, Qingdao 266071, China

5. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China

Abstract

With the help of the known Lie algebra, a type of new 8-dimensional matrix Lie algebra is constructed in the paper. By using the 8-dimensional matrix Lie algebra, the nonlinear integrable couplings of the Levi hierarchy and the Wadati-Konno-Ichikawa (WKI) hierarchy are worked out, which are different from the linear integrable couplings. Based on the variational identity, the Hamiltonian structures of the above hierarchies are derived.

Funder

Strategic Pioneering Program of Chinese Academy of Sciences

Publisher

Hindawi Limited

Subject

Applied Mathematics,Analysis

Link

http://downloads.hindawi.com/journals/aaa/2014/678725.pdf

Reference16 articles.

1. Integrable theory of the perturbation equations

2. Integrable couplings of soliton equations by perturbations I: A general theory and application to the KDV hierarchy

3. Two pairs of Lie algebras and the integrable couplings as well as the Hamiltonian structure of the Yang hierarchy