Two New Integrable Hierarchies and Their Nonlinear Integrable Couplings - Journal of Applied Mathematics and Physics

JAMP > Vol.6 No.6, June 2018

Journal of Applied Mathematics and Physics

Volume 6, Issue 6 (June 2018)

ISSN Print: 2327-4352 ISSN Online: 2327-4379

Google-based Impact Factor: 0.70 Citations

Two New Integrable Hierarchies and Their Nonlinear Integrable Couplings ()

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Download as PDF (Size: 415KB) PP. 1346-1362

DOI: 10.4236/jamp.2018.66113 645 Downloads 1,262 Views Citations

Author(s)

Hui Chang, Yuxia Li^*

Affiliation(s)

College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao, China.

ABSTRACT

By introducing an invertible linear transform, a new Lie algebra G is obtained from the Lie algebra H. Making use of the compatibility conditions of the respective isospectral problems, a generalized NLS-MKdV hierarchy and a new integrable soliton hierarchy are achieved by using the trace identity or the variational identity. Then, two special non-semisimple Lie algebras

and

are explicitly conducted. As an application, the nonlinear continuous integrable couplings of the obtained integrable systems as well as their bi-Hamiltonian structures are established, respectively.

KEYWORDS

Non-Semisimple Lie algebra, Nonlinear Integrable Coupling, Hamiltonian Structure, Trace Identity, Variational Identity

Share and Cite:

Chang, H. and Li, Y. (2018) Two New Integrable Hierarchies and Their Nonlinear Integrable Couplings. Journal of Applied Mathematics and Physics, 6, 1346-1362. doi: 10.4236/jamp.2018.66113.

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