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

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.

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.

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 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).

The gauge transformations of the constrainedq-deformed KP hierarchy

2018 ◽  
Vol 32 (16) ◽  
pp. 1850176 ◽  
Author(s):  
Lumin Geng ◽  
Huizhan Chen ◽  
Na Li ◽  
Jipeng Cheng
Keyword(s):  
Gauge Transformation ◽  
Generating Functions ◽  
Kp Hierarchy ◽  
Gauge Transformations ◽  
Lax Operator ◽  
Usual Case ◽  
Additional Constraints

In this paper, we mainly study the gauge transformations of the constrained q-deformed Kadomtsev–Petviashvili (q-KP) hierarchy. Different from the usual case, we have to consider the additional constraints on the Lax operator of the constrained q-deformed KP hierarchy, since the form of the Lax operator must be kept when constructing the gauge transformations. For this reason, the selections of generating functions in elementary gauge transformation operators [Formula: see text] and [Formula: see text] must be very special, which are from the constraints in the Lax operator. At last, we consider the successive applications of n-step of [Formula: see text] and k-step of [Formula: see text] gauge transformations.

The gauge transformations generated by the wave functions in the constrained modified KP hierarchy

2020 ◽  
Vol 34 (18) ◽  
pp. 2050205
Author(s):  
Yi Yang ◽  
Jipeng Cheng
Keyword(s):  
Gauge Transformation ◽  
Generating Functions ◽  
Wave Functions ◽  
Kp Hierarchy ◽  
Gauge Transformations

There are two ways to choose the generating functions of the gauge transformations [Formula: see text] and [Formula: see text], when dicussing the gauge transformations for the constrained modified KP hierarchy. The first is to select the (adjoint) eigenfunctions, while the second is the (adjoint) wave functions. In this paper, we will mainly discuss the gauge transformations obtained by the second method. The corresponding successive applications are considered. Also, we investigate the results of the gauge transformation derived through the union of these two methods.

Solving the constrained KP hierarchy by gauge transformations

1997 ◽  
Vol 38 (8) ◽  
pp. 4128-4137 ◽  
Author(s):  
Ling-Lie Chau ◽  
Jiin-Chang Shaw ◽  
Ming-Hsien Tu
Keyword(s):  
Kp Hierarchy ◽  
Gauge Transformations

Poisson Brackets & Angular Momentum

2018 ◽  
Author(s):  
Peter Mann
Keyword(s):  
Generating Functions ◽  
First Integrals ◽  
Lagrangian Mechanics ◽  
Poisson Brackets ◽  
Coordinate Transformations ◽  
Canonical Transformations ◽  
Gauge Transformations ◽  
The Third ◽  
Point Transformations ◽  
Canonical Coordinate

This chapter discusses canonical transformations and gauge transformations and is divided into three sections. In the first section, canonical coordinate transformations are introduced to the reader through generating functions as the extension of point transformations used in Lagrangian mechanics, with the harmonic oscillator being used as an example of a canonical transformation. In the second section, gauge theory is discussed in the canonical framework and compared to the Lagrangian case. Action-angle variables, direct conditions, symplectomorphisms, holomorphic variables, integrable systems and first integrals are examined. The third section looks at infinitesimal canonical transformations resulting from functions on phase space. Ostrogradsky equations in the canonical setting are also detailed.

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