MÖBIUS-TODA HIERARCHY AND ITS INTEGRABILITY

doi:10.1016/S0252-9602(17)30063-2

数学物理学报(英文版) ›› 2017, Vol. 37 ›› Issue (4): 1151-1161.doi: 10.1016/S0252-9602(17)30063-2

MÖBIUS-TODA HIERARCHY AND ITS INTEGRABILITY

李传忠

Department of Mathematics, Ningbo University, Ningbo 315211, China

收稿日期:2016-02-01 修回日期:2016-09-24 出版日期:2017-08-25 发布日期:2017-08-25
作者简介:Chuanzhong LI,E-mail:lichuanzhong@nbu.edu.cn
基金资助:
This work was supported by the National Natural Science Foundation of China (11571192), the Natural Science Foundation of Ningbo (2015A610157) and K. C. Wong Magna Fund in Ningbo University.

MÖBIUS-TODA HIERARCHY AND ITS INTEGRABILITY

Chuanzhong LI

Department of Mathematics, Ningbo University, Ningbo 315211, China

Received:2016-02-01 Revised:2016-09-24 Online:2017-08-25 Published:2017-08-25
About author:Chuanzhong LI,E-mail:lichuanzhong@nbu.edu.cn
Supported by:
This work was supported by the National Natural Science Foundation of China (11571192), the Natural Science Foundation of Ningbo (2015A610157) and K. C. Wong Magna Fund in Ningbo University.

摘要/Abstract

摘要：

In this paper, we construct a new integrable equation called Möbius-Toda equation which is a generalization of q-Toda equation. Meanwhile its soliton solutions are constructed to show its integrable property. Further the Lax pairs of the Möbius-Toda equation and a whole integrable Möbius-Toda hierarchy are also constructed. To show the integrability, the bi-Hamiltonian structure and tau symmetry of the Möbius-Toda hierarchy are given and this leads to the existence of the tau function.

关键词: Möbius-Toda equation, soliton solutions, Lax equation, Möbius-Toda hierarchy, tau function

Abstract:

Key words: Möbius-Toda equation, soliton solutions, Lax equation, Möbius-Toda hierarchy, tau function

李传忠. MÖBIUS-TODA HIERARCHY AND ITS INTEGRABILITY[J]. 数学物理学报(英文版), 2017, 37(4): 1151-1161.

Chuanzhong LI. MÖBIUS-TODA HIERARCHY AND ITS INTEGRABILITY[J]. Acta mathematica scientia,Series B, 2017, 37(4): 1151-1161.

参考文献

[1] Toda M. Vibration of a chain with nonlinear interaction. J Phys Soc Jpn, 1967, 22:431-436
[2] Toda M. Nonlinear Waves and Solitons. Dordrecht, Holland:Kluwer Academic Publishers, 1989
[3] Ueno K, Takasaki K. Toda lattice hierarchy//Group Representations and Systems of Differential Equations (Tokyo, 1982). Adv Stud Pure Math, 4. Amsterdam:North-Holland, 1984:1-95
[4] Witten E. Two-dimensional gravity and intersection theory on moduli space. Surveys Differ Geom, 1991, 1:243-310
[5] Dubrovin B A. Geometry of 2D topological field theories//Integrable Systems and Quantum Groups (Montecatini Terme, 1993). Lecture Notes in Math, 1620. Berlin:Springer, 1996:120-348
[6] Carlet G, Dubrovin B, Zhang Y. The extended Toda hierarchy. Moscow Math J, 2004, 4:313-332
[7] Carlet G. The extended bigraded Toda hierarchy. J Phys A, 2006, 39:9411-9435
[8] Li C Z, He J S, Wu K, Cheng Y. Tau function and Hirota bilinear equations for the extended bigraded Toda Hierarchy. J Math Phys, 2010, 51:043514
[9] Li C Z. Solutions of bigraded Toda hierarchy. J Phys A, 2011, 44:255201
[10] Li C Z, He J S. Dispersionless bigraded Toda hierarchy and its additional symmetry. Reviews Math Phys, 2012, 24:1230003
[11] Li C Z, He J S, Su Y C. Block type symmetry of bigraded Toda hierarchy. J Math Phys, 2012, 53:013517
[12] Li C Z, He J S, The extended Z_N-Toda hierarchy. Theor Math Phys, 2015, 185:1614-1635
[13] Meng A, Li C Z, Huang S. Integrability on generalized q-Toda equation and hierarchy. J Nonlinear Math Phys, 2014, 21:429-441
[14] Li C Z, Sato theory on the q-Toda hierarchy and its extension. Chaos Solitons Fract, 2015, 76:10-23
[15] Kac V G, van de Leur J W. The n-component KP hierarchy and representation theory. J Math Phys, 2003, 44:3245
[16] Mas J, Seco M. The algebra of q-pseudodifferential symbols and the q-W_KP⁽ⁿ⁾ algebra. J Math Phys, 1996, 37:6510-6529
[17] Tu M H. q-deformed KP hierarchy:its additional symmetries and infinitesimal Bäcklund transformations. Lett Math Phys, 1999, 49:95-103
[18] Lin R, Liu X, Zeng Y. A new extended q-deformed KP hierarchy. J Nonlinear Math Phys, 2008, 15:333-347
[19] Iliev P, Tau function solutions to a q-deformation of the KP hierarchy. Lett Math Phys, 1998, 44:187-200
[20] He J S, Li Y H, Cheng Y. q-deformed KP hierarchy and q-deformed constrained KP hierarchy. SIGMA, 2006, 2:060
[21] Tian K L, He J S, Su Y C, Cheng Y. String equations of the q-KP hierarchy. Chin Ann Math, Series B, 2011, 32:895-904
[22] Li C Z, Li T T. Virasoro symmetry of the (r, m)-component q-constrained KP hierarchy. submitted
[23] Tsuboi Z, Kuniba A. Solutions of a discretized Toda field equation for D_r from analytic Bethe ansatz. J Phys A, 1996, 29:7785-7796
[24] Silindir B. Soliton solutions of q-Toda lattice by Hirota direct method. Adv Differ Equ, 2012, 2012:121
[25] Sato M. Soliton Equations as Dynamical Systems on a Infinite Dimensional Grassmann Manifolds. RIMS Kokyuroku, 1982, 439:30-46

MÖBIUS-TODA HIERARCHY AND ITS INTEGRABILITY

MÖBIUS-TODA HIERARCHY AND ITS INTEGRABILITY

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