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Journal of Mathematical Physics / Volume 53 / Issue 1 / ARTICLES / Methods of Mathematical Physics

J. Math. Phys. 53, 013503 (2012); http://dx.doi.org/10.1063/1.3673275 (18 pages)

Super extension of Bell polynomials with applications to supersymmetric equations

Engui Fan1 and Y. C. Hon2

1School of Mathematical Sciences, Institute of Mathematics and Key Laboratory of Mathematics for Nonlinear Science, Fudan University, Shanghai 200433, People's Republic of China
2Department of Mathematics, City University of Hong Kong, Hong Kong, People's Republic of China

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(Received 29 January 2011; accepted 6 December 2011; published online 4 January 2012)

In this paper, we generalize classical Bell polynomials into super version, which are found to be effective in systematically constructing super bilinear representation, bilinear Bäcklund transformation, Lax pair, and infinite conservation laws of supersymmetric equations. We take N = 1 supersymmetric KdV equation and N = 2 supersymmetric sine-Gordon equation to illustrate this procedure.

© 2012 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. SUPER DERIVATIVES AND BILINEAR OPERATORS
  3. GENERALIZED SUPER BELL POLYNOMIALS
    1. Super Bell polynomials
    2. Generalized super binary Bell polynomials
  4. SUPERSYMMETRIC KDV EQUATION
  5. SUPERSYMMETRIC SINE-GORDON EQUATION
  6. CONCLUDING REMARKS

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KEYWORDS and PACS

Keywords

Korteweg-de Vries equation, nonlinear differential equations, partial differential equations, polynomials, solitons, supersymmetry

PACS

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.3673275

PUBLICATION DATA

ISSN

0022-2488 (print)  
1089-7658 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

For access to fully linked references, you need to log in.
    P. Ramond, Phys. Rev. D 3, 2415 (1971).

    P. Mathieu, J. Math. Phys. 29, 2499 (1988)JMAPAQ000029000011002499000001.

    S. Andrea, A. Restuccia, and A. Sotomayor, J. Math. Phys. 46, 103517 (2005)JMAPAQ000046000010103517000001.



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