Lax Pairs of Integrable Systems in Bidifferential Graded Algebras

doi:10.1088/0256-307X/37/4/040201

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 Lou^3**

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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https://cpl.iphy.ac.cn/10.1088/0256-307X/37/4/040201 OR https://cpl.iphy.ac.cn/Y2020/V37/I4/040201

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	Danda Zhang
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	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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