Supersymmetric kuper camassa - Holm equation and geodesic flow: A novel approach

Partha Guha

doi:10.1142/S0219887808002618

Supersymmetric kuper camassa - Holm equation and geodesic flow: A novel approach

Partha Guha

Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We use the logarithmic 2-cocycle and the action of V ect (S¹) on the space of pseudodifferential symbols to derive one particular type of supersymmetric KdV equation, known as Kuper-KdV equation. This equation was formulated by Kupershmidt and it is different from the Manin-Radul-Mathieu type equation. The two Super KdV equations behave differently under a supersymmetric transformation and Kupershmidt version does not preserve SUSY transformation. In this paper we study the second type of supersymmetric generalization of the Camassa-Holm equation correspoding to Kuper-KdV equation via standard embedding of super vector fields into the Lie algebra of graded pseudodifferential symbols. The natural lift of the action of superconformal group SDiff yields SDiff module. This method is particularly useful to construct Moyal quantized systems.

Original language	British English
Pages (from-to)	1-16
Number of pages	16
Journal	International Journal of Geometric Methods in Modern Physics
Volume	5
Issue number	1
DOIs	https://doi.org/10.1142/S0219887808002618
State	Published - Feb 2008

Keywords

Area preserving
Noncommutative integrable systems
Pseudodifferential symbols
Super KdV
Supersymmetry

Access to Document

10.1142/S0219887808002618

Cite this

@article{e18a3fd0447d4c8f9c86150ca5fc077f,

title = "Supersymmetric kuper camassa - Holm equation and geodesic flow: A novel approach",

abstract = "We use the logarithmic 2-cocycle and the action of V ect (S1) on the space of pseudodifferential symbols to derive one particular type of supersymmetric KdV equation, known as Kuper-KdV equation. This equation was formulated by Kupershmidt and it is different from the Manin-Radul-Mathieu type equation. The two Super KdV equations behave differently under a supersymmetric transformation and Kupershmidt version does not preserve SUSY transformation. In this paper we study the second type of supersymmetric generalization of the Camassa-Holm equation correspoding to Kuper-KdV equation via standard embedding of super vector fields into the Lie algebra of graded pseudodifferential symbols. The natural lift of the action of superconformal group SDiff yields SDiff module. This method is particularly useful to construct Moyal quantized systems.",

keywords = "Area preserving, Noncommutative integrable systems, Pseudodifferential symbols, Super KdV, Supersymmetry",

author = "Partha Guha",

year = "2008",

month = feb,

doi = "10.1142/S0219887808002618",

language = "British English",

volume = "5",

pages = "1--16",

journal = "International Journal of Geometric Methods in Modern Physics",

issn = "0219-8878",

publisher = "World Scientific Publishing Co. Pte Ltd",

number = "1",

}

TY - JOUR

T1 - Supersymmetric kuper camassa - Holm equation and geodesic flow

T2 - A novel approach

AU - Guha, Partha

PY - 2008/2

Y1 - 2008/2

N2 - We use the logarithmic 2-cocycle and the action of V ect (S1) on the space of pseudodifferential symbols to derive one particular type of supersymmetric KdV equation, known as Kuper-KdV equation. This equation was formulated by Kupershmidt and it is different from the Manin-Radul-Mathieu type equation. The two Super KdV equations behave differently under a supersymmetric transformation and Kupershmidt version does not preserve SUSY transformation. In this paper we study the second type of supersymmetric generalization of the Camassa-Holm equation correspoding to Kuper-KdV equation via standard embedding of super vector fields into the Lie algebra of graded pseudodifferential symbols. The natural lift of the action of superconformal group SDiff yields SDiff module. This method is particularly useful to construct Moyal quantized systems.

AB - We use the logarithmic 2-cocycle and the action of V ect (S1) on the space of pseudodifferential symbols to derive one particular type of supersymmetric KdV equation, known as Kuper-KdV equation. This equation was formulated by Kupershmidt and it is different from the Manin-Radul-Mathieu type equation. The two Super KdV equations behave differently under a supersymmetric transformation and Kupershmidt version does not preserve SUSY transformation. In this paper we study the second type of supersymmetric generalization of the Camassa-Holm equation correspoding to Kuper-KdV equation via standard embedding of super vector fields into the Lie algebra of graded pseudodifferential symbols. The natural lift of the action of superconformal group SDiff yields SDiff module. This method is particularly useful to construct Moyal quantized systems.

KW - Area preserving

KW - Noncommutative integrable systems

KW - Pseudodifferential symbols

KW - Super KdV

KW - Supersymmetry

UR - http://www.scopus.com/inward/record.url?scp=44049101730&partnerID=8YFLogxK

U2 - 10.1142/S0219887808002618

DO - 10.1142/S0219887808002618

M3 - Article

AN - SCOPUS:44049101730

SN - 0219-8878

VL - 5

SP - 1

EP - 16

JO - International Journal of Geometric Methods in Modern Physics

JF - International Journal of Geometric Methods in Modern Physics

IS - 1

ER -

Supersymmetric kuper camassa - Holm equation and geodesic flow: A novel approach

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this