THE INTEGRAL TYPE GAUGE TRANSFORMATION AND THE ADDITIONAL SYMMETRY FOR THE CONSTRAINED KP HIERARCHY

doi:10.1016/S0252-9602(15)30043-6

数学物理学报(英文版) ›› 2015, Vol. 35 ›› Issue (5): 1111-1121.doi: 10.1016/S0252-9602(15)30043-6

THE INTEGRAL TYPE GAUGE TRANSFORMATION AND THE ADDITIONAL SYMMETRY FOR THE CONSTRAINED KP HIERARCHY

程级鹏¹, 贺劲松²

1. Department of Mathematics, China University of Mining and Technology, Xuzhou 221116, China;
2. Department of Mathematics, Ningbo University, Ningbo 315211, China

收稿日期:2014-01-08 修回日期:2015-03-11 出版日期:2015-09-01 发布日期:2015-09-01
通讯作者: Jingsong HE E-mail:hejingsong@nbu.edu.cn
作者简介:Jipeng CHENG, E-mail: chengjp@cumt.edu.cn, chengjp@mail.ustc.edu.cn; Jingsong HE, E-mail: hejingsong@nbu.edu.cn
基金资助:
This work is supported by the Fundamental Research Funds for the Central Universities (2015QNA43).

THE INTEGRAL TYPE GAUGE TRANSFORMATION AND THE ADDITIONAL SYMMETRY FOR THE CONSTRAINED KP HIERARCHY

Jipeng CHENG¹, Jingsong HE²

1. Department of Mathematics, China University of Mining and Technology, Xuzhou 221116, China;
2. Department of Mathematics, Ningbo University, Ningbo 315211, China

Received:2014-01-08 Revised:2015-03-11 Online:2015-09-01 Published:2015-09-01
Contact: Jingsong HE E-mail:hejingsong@nbu.edu.cn
Supported by:
This work is supported by the Fundamental Research Funds for the Central Universities (2015QNA43).

摘要/Abstract

摘要：

In this paper, the compatibility between the integral type gauge transformation and the additional symmetry of the constrained KP hierarchy is given. And the string-equation constraint in matrix models is also derived.

关键词: constrained KP hierarchy, integral type gauge transformation, additional symmetry

Abstract:

Key words: constrained KP hierarchy, integral type gauge transformation, additional symmetry

中图分类号:

35Q53

程级鹏, 贺劲松. THE INTEGRAL TYPE GAUGE TRANSFORMATION AND THE ADDITIONAL SYMMETRY FOR THE CONSTRAINED KP HIERARCHY[J]. 数学物理学报(英文版), 2015, 35(5): 1111-1121.

Jipeng CHENG, Jingsong HE. THE INTEGRAL TYPE GAUGE TRANSFORMATION AND THE ADDITIONAL SYMMETRY FOR THE CONSTRAINED KP HIERARCHY[J]. Acta mathematica scientia,Series B, 2015, 35(5): 1111-1121.

参考文献

[1] Date E, Jimbo M, Kashiwara M, Miwa T. Transformation groups for soliton equations//Jimbo M, Miwa T. Nonlinear Integrable Systems-Classical Theory and Quantum Theory. Singapore:World Scientific, 1983:39-119
[2] Dickey L A. Soliton Equations and Hamiltonian Systems. 2nd ed. Singapore:World Scientific, 2003
[3] Witten E. Two dimensional gravity and intersection theory on moduli space. Surveys Diff Geom, 1991, 1:243-310
[4] Kontsevich M. Intersection theory on the moduli space of curves and the matrix Airy function. Comm Math Phys, 1992, 147:1-23
[5] Adler M, van Moerbeke P. A matrix integral solutionto two-dimensional W_p gravity. Comm Math Phys, 1992, 147:25-56
[6] Kac V. Infinite Dimensional Lie Algebras. 3rd ed. Cambridge Univ Press, 1990
[7] Jimbo M, Miwa T. Solitons and infinite dimensional Lie algebras. Publ RIMS, Kyoto Univ, 1983, 19:943-1001
[8] Cheng Y, Li Y S. The constraint of the KP equation and its special solutions. Phys Lett A, 1991, 157:22-26
[9] Konopelchenko B, Sidorenko J, Strampp W. (1+1)-dimensional integrable systems as symmetry constraints of (2+1)-dimensional systems. Phys Lett A, 1991, 157:17-21
[10] Cheng Y. Constraints of the KP hierarchy. J Math Phys, 1992, 33:3774-3782
[11] Li C Z, Tian K L, He J S, Cheng Y. The recursion operator for a constrained CKP hierarchy. Acta Math Sci, 2011, 31B(4):1295-1302
[12] Chau L L, Shaw J C, Yen H C. Solving the KP hierarchy by gauge transformations. Comm Math Phys, 1992, 149:263-278
[13] Oevel W. Darboux theorems and Wronskian formulas for integrable system I:constrained KP flows. Physica A, 1993, 195:533-576
[14] Aratyn H, Nissimov E, Pacheva S. Darboux-Backlund solutions of SL(p, q) KP-KdV hierarchies, constrained generalized Toda lattices, and two-matrix string model. Phys Lett A, 1995, 201:293-305
[15] Chau L L, Shaw J C, Tu M H. Solving the constrained KP hierarchy by gauge transformations. J Math Phys, 1997,38:4128-4137
[16] Willox R, Loris I, Gilson C R. Binary Darboux transformations for constrained KP hierarchies. Inverse Problems, 1997, 13:849-865
[17] He J S, Li Y S and Cheng Y. Two choices of the gauge transformation for the AKNS hierarchy through the constrained KP hierarchy. J Math Phys, 2003, 44:3928-3960
[18] Nimmo J J C. Darboux transformations from reductions of the KP hierarchy//Makhankov V G, Bishop A R, Holm D D. Nonlinear Evolution Equations and Dynamical Systems. Singapore:World Scientific, 1995:168-177
[19] He J S, Wu Z W, Cheng Y. Gauge transformations for the constrained CKP and BKP hierarchies. J Math Phys, 2007, 48:113519
[20] Oevel W. Darboux transformations for integrable lattice systems//Alfinito E, Martina L, Pempinelli F. Nonlinear Physics:Theory and Experiment. Singapore:World Scientific, 1996:233-240
[21] Liu S W, Cheng Y, He J S. The determinant representation of the gauge transformation for the discrete KP hierarchy. Sci China Math, 2010, 53:1195-1206
[22] Tu M H, Shaw J C, and Lee C R. On Darboux-Backlund transformations for the q-deformed Korteweg-de Vries hierarchy. Lett Math Phys, 1999, 49:33-45
[23] He J S, Li Y H and Cheng Y. q-deformed KP hierarchy and q-deformed constrained KP hierarchy. SIGMA, 2006, 2:060
[24] Chen H H, Lee Y C and Lin J E. On a new hierarchy of symmetry for the Kadomtsev-Petviashvili equation. Physica D, 1983, 9:439-445
[25] Orlov A Yu, Schulman E I. Additional symmetries for integrable systems and conformal algebra repesentation. Lett Math Phys, 1993, 12:171-179
[26] Adler M, Shiota T, van Moerbeke P. A Lax representation for the vertex operator and the central extension. Comm Math Phys, 1995, 171:547-588
[27] Dickey L A. On additional symmetries of the KP hierarchy and Sato's Bäcklund transformation. Comm Math Phys, 1995, 167:227-233
[28] Takasaki K. Toda lattice hierarchy and generalized string equations. Comm Math Phys, 1996, 181:131-156
[29] Tu M H. On the BKP hierarchy:Additional symmetries, Fay identity and Adler-Shiotavan Moerbeke formula. Lett Math Phys, 2007, 81:91-105
[30] He J S, Tian K L, Foerster A, Ma W X. Additional symmetries and string equation of the CKP hierarchy. Lett Math Phys, 2007, 81:119-134
[31] Cheng J P, Tian K L, He J S. The additional symmetries for the BTL and CTL hierarchies. J Math Phys, 2011, 52:053515
[32] Li C Z, He J S. Dispersionless bigraded Toda hierarchy and its additional symmetry. Rev Math Phys, 2012, 24:1230003
[33] Li C Z, He J S, Su Y C. Block type symmetry of bigraded Toda hierarchy. J Math Phys, 2012, 53:013517
[34] van Moerbeke P. Integrable fundations of string theory//Babelon O, Cartier P, Kosmann-Schwarzbach Y. Lectures on Integrable Systems. Singapore:World Scientific, 1994:163-267
[35] Aratyn H, Nissimov E, Pacheva S. Virasoro symmetry of constrained KP hierarchies. Phys Lett A, 1997, 228:164-175
[36] Tian K L, He J S, Cheng J P, Cheng Y. Additional symmetries of constrained CKP and BKP hierarchies. Sci China Math, 2011, 54:257-268
[37] Shen H F, Tu M H. On the constrained B-type Kadomtsev-Petviashvili hierarchy:Hirota bilinear equations and Virasoro symmetry. J Math Phys, 2011, 52:032704
[38] Oevel W and Rogers C. Gauge transformations and reciprocal links in 2+1 dimensions. Rev Math Phys, 1993, 5:299-330
[39] Enriquez B, Orlov A Yu, Rubtsov V N. Dispersionful analogues of Benney's equations and N-wave systems. Inverse Problems, 1996, 12:241-250

THE INTEGRAL TYPE GAUGE TRANSFORMATION AND THE ADDITIONAL SYMMETRY FOR THE CONSTRAINED KP HIERARCHY

THE INTEGRAL TYPE GAUGE TRANSFORMATION AND THE ADDITIONAL SYMMETRY FOR THE CONSTRAINED KP HIERARCHY

PDF (PC)

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 14

Metrics

本文评价

推荐阅读 10

[1]	霍朝辉. GLOBAL WELL-POSEDNESS IN ENERGY SPACE OF SMALL AMPLITUDE SOLUTIONS FOR KLEIN-GORDON-ZAKHAROV EQUATION IN THREE SPACE DIMENSION[J]. 数学物理学报(英文版), 2016, 36(4): 1117-1152.
[2]	傅仰耿, 刘正荣, 唐昊. NON-UNIFORM DEPENDENCE ON INITIAL DATA FOR THE MODIFIED CAMASSA-HOLM EQUATION ON THE LINE[J]. 数学物理学报(英文版), 2014, 34(6): 1781-1794.
[3]	王宏伟. LOCAL WELL-POSEDNESS IN SOBOLEV SPACES WITH NEGATIVE INDICES FOR A SEVENTH ORDER DISPERSIVE EQUATION[J]. 数学物理学报(英文版), 2014, 34(1): 199-208.
[4]	陈正争, 肖清华. NONLINEAR STABILITY OF PLANAR SHOCK PROFILES FOR THE GENERALIZED KdV-BURGERS EQUATION IN SEVERAL DIMENSIONS[J]. 数学物理学报(英文版), 2013, 33(6): 1531-1550.
[5]	周寿明, 穆春来, 王良展. SELF-SIMILAR SOLUTIONS AND BLOW-UP PHENOMENA FOR A TWO-COMPONENT SHALLOW WATER SYSTEM[J]. 数学物理学报(英文版), 2013, 33(3): 821-829.
[6]	闫威, 李用声. ILL-POSEDNESS OF MODIFIED KAWAHARA EQUATION AND KAUP-KUPERSHMIDT EQUATION[J]. 数学物理学报(英文版), 2012, 32(2): 710-716.
[7]	李传忠, 田可雷, 贺劲松, 程艺. THE RECURSION OPERATOR FOR A CONSTRAINED CKP HIERARCHY[J]. 数学物理学报(英文版), 2011, 31(4): 1295-1302.
[8]	李用声, 杨兴雨. GLOBAL WELL-POSEDNESS FOR A FIFTH-ORDER SHALLOW WATER EQUATION ON THE CIRCLE[J]. 数学物理学报(英文版), 2011, 31(4): 1303-1317.
[9]	谭忠, 王焰金. STRONG SOLUTIONS FOR THE INCOMPRESSIBLE FLUID MODELS OF KORTEWEG TYPE[J]. 数学物理学报(英文版), 2010, 30(3): 799-809.
[10]	江新华, 王振. PERTURBED PERIODIC SOLUTION FOR BOUSSINESQ EQUATION[J]. 数学物理学报(英文版), 2009, 29(3): 705-722.
[11]	付一平; 郭柏灵. ALMOST PERIODIC SOLUTION OF ONE DIMENSIONAL VISCOUS CAMASSA-HOLM EQUATION[J]. 数学物理学报(英文版), 2007, 27(1): 117-124.
[12]	陈翰林, 郭柏林. THE INVARIANT MANIFOLDS FOR A PERTURBED QUINTIC-CUBIC SCHR¨\|ODINGER EQUATION 1[J]. 数学物理学报(英文版), 2004, 24(4): 536-548.
[13]	丁夏畦, 丁毅. VISCOSITY METHOD OF A NON-HOMOGENEOUS BURGERS EQUATION[J]. 数学物理学报(英文版), 2003, 23(4): 567-.
[14]	潘留仙, 颜家壬, 周光辉. A DIRECT APPROACH TO THE SOLITON PERTURBATION FOR KdV-MKdV EQUATION[J]. 数学物理学报(英文版), 2003, 23(3): 356-.