Chin. Phys. Lett.  2020, Vol. 37 Issue (4): 040201    DOI: 10.1088/0256-307X/37/4/040201
GENERAL |
Lax Pairs of Integrable Systems in Bidifferential Graded Algebras
Danda Zhang1, Da-Jun Zhang2, Sen-Yue Lou3**
1School of Mathematics and Statistics, Ningbo University, Ningbo 315211
2Department of Mathematics, Shanghai University, Shanghai 200444
3School of Physical Science and Technology, Ningbo University, Ningbo 315211
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Danda Zhang, Da-Jun Zhang, Sen-Yue Lou 2020 Chin. Phys. Lett. 37 040201
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Abstract Lax pairs regarded as foundations of the inverse scattering methods play an important role in integrable systems. In the framework of bidifferential graded algebras, we propose a straightforward approach to constructing the Lax pairs of integrable systems in functional environment. Some continuous equations and discrete equations are presented.
Received: 11 December 2019      Published: 24 March 2020
PACS:  02.30.Ik (Integrable systems)  
  02.30.Jr (Partial differential equations)  
  47.20.Ky (Nonlinearity, bifurcation, and symmetry breaking)  
Fund: Supported by the National Natural Science Foundation of China (Nos. 11875040, 11435005, 11975131, and 11801289), and the K. C. Wong Magna Fund in Ningbo University.
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http://cpl.iphy.ac.cn/10.1088/0256-307X/37/4/040201       OR      http://cpl.iphy.ac.cn/Y2020/V37/I4/040201
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Danda Zhang
Da-Jun Zhang
Sen-Yue Lou
[1]Ablowitz M J, Chakravarty S and Halburd R G 2003 J. Math. Phys. 44 3147
[2]Dimakis A and Müller-Hoissen F 2000 Rep. Math. Phys. 46 203
[3]Dimakis A and Müller-Hoissen F 2000 J. Phys. A 33 957
[4]Crampin M, Sarlet W and Thompson G 2000 J. Phys. A 33 8755
[5]Dimakis A and Müller-Hoissen F 2010 SIGMA 6 055
[6]Dimakis A and Müller-Hoissen 2010 Inverse Probl. 26 095007
[7]Chvartatskyi O, Müller-Hoissen F and Stoilov N 2015 J. Math. Phys. 56 103512
[8]Dimakis A and Müller-Hoissen F 2000 J. Phys. A 33 6579
[9]Dimakis A and Müller-Hoissen F 2009 Discr. Cont. Dyn. Syst. Suppl. 2009 208
[10]Dimakis A and Müller-Hoissen F 2013 SIGMA 9 009
[11]Chvartatskyi O, Dimakis A and Müller-Hoissen F 2015 Lett. Math. Phys. 106 08
[12]Zhao S L, Zhang D J and Shi Y 2012 Chin. Ann. Math. Ser. B 33 259
[13]Zhang D J and Zhao S L 2013 Stud. Appl. Math. 131 72
[14]Xu D D, Zhang D J and Zhao S L 2014 J. Nonlinear Math. Phys. 21 382
[15]Dimakis A and Müller-Hoissen F 2018 arXiv:1801.00589
[16]Lüscher M and Pohlmeyer K 1978 Nucl. Phys. B 137 46
[17]Brézin E, Itzykson C, Zinn-Justin J and Zuber J B 1979 Phys. Lett. B 82 442
[18]Fu W and Nijhoff F W 2017 Proc. R. Soc. A 473 20160915
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