AN ABLOWITZ-LADIK INTEGRABLE LATTICE HIERARCHY WITH MULTIPLE POTENTIALS

doi:10.1007/s10473-020-0306-3

数学物理学报(英文版) ›› 2020, Vol. 40 ›› Issue (3): 670-678.doi: 10.1007/s10473-020-0306-3

AN ABLOWITZ-LADIK INTEGRABLE LATTICE HIERARCHY WITH MULTIPLE POTENTIALS

马文秀^1,2,3,4,5,6

1 School of Mathematics, South China University of Technology, Guangzhou 510640, China;
2 Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia;
3 Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620, USA;
4 Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China;
5 College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China;
6 Department of Mathematical Sciences, North-West University, Mafikeng Campus, Mmabatho 2735, South Africa

收稿日期:2018-11-11 出版日期:2020-06-25 发布日期:2020-07-17
作者简介:Wen-Xiu MA,E-mail:mawx@cas.usf.edu
基金资助:
The work was supported in part by NSF (DMS-1664561), NSFC (11975145 and 11972291), the Natural Science Foundation for Colleges and Universities in Jiangsu Province (17KJB110020), and Emphasis Foundation of Special Science Research on Subject Frontiers of CUMT (2017XKZD11).

AN ABLOWITZ-LADIK INTEGRABLE LATTICE HIERARCHY WITH MULTIPLE POTENTIALS

Wen-Xiu MA^1,2,3,4,5,6

1 School of Mathematics, South China University of Technology, Guangzhou 510640, China;
2 Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia;
3 Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620, USA;
4 Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China;
5 College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China;
6 Department of Mathematical Sciences, North-West University, Mafikeng Campus, Mmabatho 2735, South Africa

Received:2018-11-11 Online:2020-06-25 Published:2020-07-17
Supported by:
The work was supported in part by NSF (DMS-1664561), NSFC (11975145 and 11972291), the Natural Science Foundation for Colleges and Universities in Jiangsu Province (17KJB110020), and Emphasis Foundation of Special Science Research on Subject Frontiers of CUMT (2017XKZD11).

摘要/Abstract

摘要： Within the zero curvature formulation, a hierarchy of integrable lattice equations is constructed from an arbitrary-order matrix discrete spectral problem of Ablowitz-Ladik type. The existence of infinitely many symmetries and conserved functionals is a consequence of the Lax operator algebra and the trace identity. When the involved two potential vectors are scalar, all the resulting integrable lattice equations are reduced to the standard Ablowitz-Ladik hierarchy.

关键词: Integrable lattice, discrete spectral problem, symmetry and conserved functional

Abstract: Within the zero curvature formulation, a hierarchy of integrable lattice equations is constructed from an arbitrary-order matrix discrete spectral problem of Ablowitz-Ladik type. The existence of infinitely many symmetries and conserved functionals is a consequence of the Lax operator algebra and the trace identity. When the involved two potential vectors are scalar, all the resulting integrable lattice equations are reduced to the standard Ablowitz-Ladik hierarchy.

Key words: Integrable lattice, discrete spectral problem, symmetry and conserved functional

中图分类号:

35Q51

马文秀. AN ABLOWITZ-LADIK INTEGRABLE LATTICE HIERARCHY WITH MULTIPLE POTENTIALS[J]. 数学物理学报(英文版), 2020, 40(3): 670-678.

Wen-Xiu MA. AN ABLOWITZ-LADIK INTEGRABLE LATTICE HIERARCHY WITH MULTIPLE POTENTIALS[J]. Acta mathematica scientia,Series B, 2020, 40(3): 670-678.

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AN ABLOWITZ-LADIK INTEGRABLE LATTICE HIERARCHY WITH MULTIPLE POTENTIALS

AN ABLOWITZ-LADIK INTEGRABLE LATTICE HIERARCHY WITH MULTIPLE POTENTIALS

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