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A HIERARCHY OF HAMILTONIAN EQUATIONS ASSOCIATED WITH THE MODIFIED JAULENT–MIODEK HIERARCHY

HAI-YONG DING

School of Remote Sensing, Nanjing University of Information Science and Technology, Nanjing 210044, China

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HONG-XIANG YANG

College of Information Science and Technology, Taishan College, Taian 271021, China

Corresponding author.

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YE-PENG SUN

School of Statistics and Mathematics, Shandong Economic University, Jinan 250014, China

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, and

LI-LI ZHU

College of Information Science and Technology, Taishan College, Taian 271021, China

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https://doi.org/10.1142/S0217984910022226Cited by:1 (Source: Crossref)

Abstract

By considering a new four-by-four matrix eigenvalue problem, a hierarchy of Lax integrable evolution equations with four potentials is derived. The Hamiltonian structures of the resulting hierarchy are established by means of the generalized trace identity. The Liouville integrability for the hierarchy of the resulting Hamiltonian equations is presented.

Keywords:

PACS: 02.30.Ik, 05.45.Yv

References

M. J. Ablowitz and P. A. Clarkson , Solitons, Nonlinear Evolation Equations and Inverse Scattering ( Cambridge University Press , England , 1992 ) . Google Scholar
C. H. Gu , Soliton Theory and Its Application ( Springer , Berlin , 1995 ) . Crossref, Google Scholar
D. Y. Chen , Soliton Introduction ( Science Press , Beijing , 2006 ) . Google Scholar
C. W. Cao and X. G. Geng, J. Math. Phys. 32, 2323 (1991). Crossref, Web of Science, ADS, Google Scholar
G. Z. Tu, J. Math. Phys. 30, 330 (1989). Crossref, Web of Science, ADS, Google Scholar
W. X. Ma, Chin. Ann. Math. A 13, 115 (1992). Google Scholar
X. B. Hu, Northeast. Math. J. 6, 187 (1990). Google Scholar
M. Antonowicz and A. P. Fordy, Commun. Math. Phys. 124, 465 (1989). Crossref, Web of Science, ADS, Google Scholar
X. X. Xu, Phys. Lett. A 301, 250 (2002). Crossref, Web of Science, ADS, Google Scholar
W. X. Ma, Appl. Math A. J. Chinese Universities 8 (1993) 28–35 (in Chinese); W. X. Ma and M. Pavlov, Phys. Lett. A 246 (1998) 511–522; W. X. Ma, J. Phys. A: Math. Gen. 31 (1998) 7279–7289; W. X. Ma, J. Phys. A: Math. Gen. 31 (1998) 7585–7591 . Google Scholar
W. X. Ma and B. Fuchssteiner, Chaos, Soliton & Fractals 7, 1227 (1996). Crossref, Web of Science, ADS, Google Scholar
W. X. Ma, Phys. Lett. A 316 (2003) 72–76; W. X. Ma, J. Math. Phys. 46 (2005) 033507-19; W. X. Ma, X. X. Xu and Y. F. Zhang, Phys. Lett. A 351 (2006) 125–130; W. X. Ma, X. X. Xu and Y. F. Zhang, J. Math. Phys. 47 (2006) 053501-16 . Google Scholar
W. X. Ma and M. Chen, J. Phys. A: Math. Gen. 39, 10787 (2006). Crossref, Google Scholar
X. X. Xu, H. X. Yang and W. L. Cao, Int. J. Mod. Phys. Lett. B 22, 4027 (2008). Link, Web of Science, ADS, Google Scholar
Y. F. Zhang, Mod. Phys. Lett. B 21(1) (2007) 37–44; Y. F. Zhang and Y. C. Hon, Mod. Phys. Lett. B 21(30) (2007) 2063–2074; Y. F. Zhang and Y. Li, Mod. Phys. Lett. B 22(19) (2008) 1837–1850 . Google Scholar
H. H. Dong, Mod. Phys. Lett. B 20(20), 1241 (2006). Link, Web of Science, ADS, Google Scholar
T. C. Xiaet al., Physica A 343, 238 (2004). Crossref, Web of Science, ADS, Google Scholar
Y. P. Sun and D. Y. Chen, Chaos, Solitons & Fractals 29, 978 (2006). Crossref, Web of Science, ADS, Google Scholar
J. B. Chen and X. G. Geng, Chaos, Solitons & Fractals 30, 797 (2006). Crossref, Web of Science, ADS, Google Scholar
Q. P. Liu, J. Phys. A: Math. Gen. 26(23), L1239 (1993). Crossref, ADS, Google Scholar
W. X. Ma, J. S. He and Z. Y. Qin, J. Math. Phys. 49, 033511-13 (2008). Google Scholar
X. B. Hu, J. Phys. A: Math. Gen. 30, 619 (1997). Crossref, ADS, Google Scholar
X. B. Hu, J. Phys. A: Math. Gen. 27, 2497 (1994). Crossref, ADS, Google Scholar
A. R. Chowdhury and S. Roy, J. Math. Phys. 27, 2464 (1986). Crossref, Web of Science, Google Scholar
H. X. Yanget al., Mod. Phys. Lett. B 20(25), 1575 (2006). Link, Web of Science, ADS, Google Scholar