GENERALIZED N=2 SUPER KdV HIERACHIES: LIE SUPERALGEBRAIC METHODS AND SCALAR SUPER LAX FORMALISM

1992 ◽  
Vol 07 (supp01a) ◽  
pp. 419-447 ◽  
Author(s):  
TAKEO INAMI ◽  
HIROAKI KANNO
Keyword(s):  
Lie Superalgebras ◽  
Kp Hierarchy ◽  
Gauge Transformations ◽  
Lax Equations

Generalized N=2 super KdV hierarchies are constructed based on super Lax equations associated with Lie superalgebras SL(n|n)(1). The equivalence of the scalar super Lax formalism and the Lie superalgebraic method is derived by taking account of gauge transformations regarding the centre of SL(n|n)(1). We show that generalized N=2 super KdV hierarchies are related to the even reductions of the super KP hierarchy.

Some results of the BKP hierarchy as the Kupershmidt reduction of the modified KP hierarchy

2020 ◽  
pp. 2050433
Author(s):  
Yi Yang ◽  
Xiaoli Wang ◽  
Jipeng Cheng
Keyword(s):  
Gauge Transformation ◽  
Wave Functions ◽  
Kp Hierarchy ◽  
Gauge Transformations ◽  
Bkp Hierarchy

In this paper, the BKP hierarchy is viewed as the Kupershmidt reduction of the modified KP hierarchy. Then based upon this fact, the gauge transformation of the BKP hierarchy are obtained again from the corresponding results of the modified KP hierarchy. Also the constrained BKP hierarchy is constructed from the constrained modified KP hierarchy, and the corresponding gauge transformations are investigated. Particularly, it is found that there is a new kind of gauge transformations generated by the wave functions in the constrained BKP hierarchy.

scholarly journals Links between(γn,σk)-KP Hierarchy,(γn,σk)-mKP Hierarchy, and (2+1)-(γn,σk)-Harry Dym Hierarchy

2015 ◽  
Vol 2015 ◽  
pp. 1-11
Author(s):  
Yehui Huang ◽  
Yuqin Yao ◽  
Yunbo Zeng
Keyword(s):  
Time Series ◽  
Evolution Equations ◽  
Soliton Solutions ◽  
Kp Hierarchy ◽  
Gauge Transformations ◽  
New Time

The new (2+1)-(γn,σk)-Harry Dym hierarchy and(γn,σk)-mKP hierarchy with two new time seriesγnandσk, which consist ofγn-flow,σk-flow, and mixedγnandσkevolution equations of eigenfunctions, are proposed. Gauge transformations and reciprocal transformations between(γn,σk)-KP hierarchy,(γn,σk)-mKP hierarchy, and (2+1)-(γn,σk)-Harry Dym hierarchy are studied. Their soliton solutions are presented.

Solving the constrained modified KP hierarchy by gauge transformations

2018 ◽  
Vol 26 (1) ◽  
pp. 54-68 ◽  
Author(s):  
Huizhan Chen ◽  
Lumin Geng ◽  
Na Li ◽  
Jipeng Cheng
Keyword(s):  
Kp Hierarchy ◽  
Gauge Transformations

GAUGE TRANSFORMATIONS AND RECIPROCAL LINKS IN 2 + 1 DIMENSIONS

1993 ◽  
Vol 05 (02) ◽  
pp. 299-330 ◽  
Author(s):  
W. OEVEL ◽  
C. ROGERS
Keyword(s):  
Differential Operators ◽  
Bäcklund Transformations ◽  
Gauge Transformations ◽  
Pseudo Differential Operators ◽  
Backlund Transformations ◽  
Lax Equations ◽  
Sato Theory

Generalized Lax equations are considered in the spirit of Sato theory. Three decompositions of an underlying algebra of pseudo-differential operators lead, in turn, to three different classes of integrable nonlinear hierarchies. These are associated with Kadomtsev-Petviashvili, modified Kadomtsev-Petviashvili and Dym hierarchies in 2 + 1 dimensions. Miura- and auto-Bäcklund transformations are shown to originate naturally from gauge transformations of the Lax operators. General statements on reciprocal links between these hierarchies are established, which, in particular, give rise to novel reciprocal auto-Bäcklund transformations for the Dym hierarchy. These links are formulated as Darboux theorems for the associated Lax operators.

THE MODIFIED CLASSICAL YANG-BAXTER EQUATION AND SUPERSYMMETRIC GEL’FAND-DIKII BRACKETS

1993 ◽  
Vol 08 (02) ◽  
pp. 129-137 ◽  
Author(s):  
C.M. YUNG
Keyword(s):  
Pseudodifferential Operators ◽  
Lie Superalgebra ◽  
Lie Superalgebras ◽  
Baxter Equation ◽  
Poisson Brackets ◽  
Trace Form ◽  
Kp Hierarchy ◽  
Infinite Dimensional

The classical Yang-Baxter equation as formulated by Semenov-Tyan-Shanskii is generalized to the case of Lie superalgebras [Formula: see text], for Grassmann even Yang-Baxter operators ℛ. When ℛ is “unitary” with respect to a super trace form defined on [Formula: see text], we prove the existence of two natural Poisson brackets on the dual [Formula: see text]*. If [Formula: see text] is the infinite-dimensional Lie superalgebra of N=1 super pseudodifferential operators, we recover the super Gel’fand-Dikii brackets underlying the N=1 super KP hierarchy and its reductions.

Solving the KP hierarchy by gauge transformations

1992 ◽  
Vol 149 (2) ◽  
pp. 263-278 ◽  
Author(s):  
Ling-Lie Chau ◽  
J. C. Shaw ◽  
H. C. Yen
Keyword(s):  
Kp Hierarchy ◽  
Gauge Transformations

Gauge transformations of constrained discrete modified KP systems with self-consistent sources

2017 ◽  
Vol 14 (04) ◽  
pp. 1750052 ◽  
Author(s):  
Ran Huang ◽  
Tao Song ◽  
Chuanzhong Li
Keyword(s):  
Gauge Transformation ◽  
Kp Hierarchy ◽  
Gauge Transformations ◽  
Self Consistent ◽  
Basic Facts ◽  
Discrete Kp ◽  
Ghost Symmetry

In this paper, we firstly recall some basic facts about the discrete KP(d-KP) and discrete modified KP(d-mKP) hierarchies, and then we find that d-KP hierarchy and d-mKP hierarchy are linked by a gauge transformation. What’s more, we give three gauge transformation operators of the d-mKP hierarchy and give their successive applications. We further construct the ghost symmetry and use this symmetry to give the definition the d-mKP hierarchy with self-consistent sources. We also give gauge transformations of a newly defined constrained d-mKP(cd-mKP) hierarchy and the constrained d-mKP hierarchy with self-consistent sources(cd-mKPHSCSs).

scholarly journals Scaling invariance of the strict KP hierarchy

2020 ◽  
pp. 331-340
Author(s):  
Gerard F. Helminck ◽  
Elena A. Panasenko
Keyword(s):  
Standard Setting ◽  
Minimal Realization ◽  
Kp Hierarchy ◽  
Scaling Invariance ◽  
Lax Equations ◽  
Strict Kp Hierarchy

In this paper we show first of all that for solutions of the strict KP hierarchy it is sufficient to work in a standard setting. Further we discuss a minimal realization of the hierarchy and present the scaling invariance of the Lax equations of the hierarchy.

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