×

On a supersymmetric nonlinear integrable equation in \((2+1)\) dimensions. (English) Zbl 1420.37094

Summary: A supersymmetric integrable equation in \((2+1)\) dimensions is constructed by means of the approach of the homogenous space of the super Lie algebra, where the super Lie algebra \(\operatorname{osp}(3/2)\) is considered. For this \((2+1)\) dimensional integrable equation, we also derive its Bäcklund transformation.

MSC:

37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
17B80 Applications of Lie algebras and superalgebras to integrable systems
37K30 Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures
37K35 Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems
35Q53 KdV equations (Korteweg-de Vries equations)
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Candu, C.; Saleur, H., A lattice approach to the conformal OSp(2S+2/2S) supercoset sigma model. Part II: The boundary spectrum, Nucl. Phys. B, 808, 487-524 (2009) · Zbl 1192.82018
[2] Ding, X. M.; Gould, M.; Mewton, C.; Zhang, Y. Z., On osp(2/2) conformal field theories, J. Phys. A: Math. Gen, 36, 7649-7666 (2003) · Zbl 1048.81051
[3] Fordy, A. P.; Kulish, P. P., Nonlinear Schrödinger Equations and Simple Lie Algebras, Commun. Math. Phys, 89, 427-443 (1983) · Zbl 0563.35062
[4] Guo, J. F.; Wang, S. K.; Wu, K.; Yan, Z. W.; Zhao, W. Z., Integrable higher order deformations of Heisenberg supermagnetic model, J. Math. Phys, 50, 113502 (2009) · Zbl 1304.82020
[5] Kupershmidt, B. A., A super Korteweg-de Vries equation: an integrable system, Phys. Lett. A, 102, 213-215 (1984)
[6] Liu, Q. P., Darboux transformations for supersymmetric Korteweg-de Vries equations, Lett. Math. Phys, 35, 115-122 (1995) · Zbl 0834.35110
[7] Liu, Q. P.; X. B., Hu, Bilinearization of N=1 supersymmetric Korteweg-de Vries equation revisited, J. Phys. A: Math. Gen, 38, 6371-6378 (2005) · Zbl 1080.35122
[8] Liu, Q. P.; Xie, Y. F., Nonlinear superposition formula for N=1 supersymmetric KdV equation, Phys. Lett. A, 325, 139-143 (2004) · Zbl 1161.37344
[9] Makhankov, V. G.; Pashaev, O. K., Continual classical Heisenberg models defined on graded su(2,1) and su(3) algebras, J. Math. Phys, 33, 2923-2936 (1992) · Zbl 0767.35083
[10] Manin, Y.; Radul, A. O., A supersymmetric extension of the Kadomtsev-Petviashvili hierarchy, Commun. Math. Phys, 98, 65-77 (1985) · Zbl 0607.35075
[11] Mathieu, P., The Painlevé property for fermionic extensions of the Korteweg-de Vries equation, Phys. Lett. A, 128, 169, 169-171 (1988)
[12] Mathieu, P., Supersymmetric extension of the Korteweg-de Vries equation, J. Math. Phys, 29, 2499-2506 (1988) · Zbl 0665.35076
[13] Mcarthur, I. N.; Yung, C. M., Hirota bilinear form for the super-KdV hierarchy, Mod. Phys. Lett. A, 8, 1739-1745 (1993) · Zbl 1020.37574
[14] Roelofs, G. H.M.; Kersten, P. H.M., Supersymmetric extensions of the nonlinear Schrödinger equation: symmetries and coverings, J. Math. Phys, 33, 2185-2206 (1992) · Zbl 0761.35103
[15] Roelofs, G. H.M.; Van Den Hijligenberg, N. W., Prolongation structures for supersymmetric equations, J. Phys. A: Math. Gen, 23, 5117-5130 (1990) · Zbl 0734.35116
[16] Saha, M.; Roy Chowdhury, A., Supersymmetric Integrable Systems in (2+1) Dimensions and Their Backlund Transformation, Int. J. Theor. Phys, 38, 2037-2047 (1999) · Zbl 0937.37049
[17] Saleur, H.; Wehefritz-Kaufmann, B., Integrable quantum field theories with OSP(m/2n) symmetries, Nucl. Phys. B, 628, 407-441 (2002) · Zbl 0990.81055
[18] Ueno, K.; Yamada, H., Supersymmetric extension of the Kadomtsev-Petviashvili hierarchy and the universal super Grassmann manifold, Adv. Stud. Pure Math, 16, 373-426 (1988) · Zbl 0675.58045
[19] Xue, L. L.; Levi, D.; Liu, Q. P., Supersymmetric KdV equation: Darboux transformation and discrete systems, J. Phys. A: Math. Theor, 46, 502001 (2013) · Zbl 1286.35224
[20] Yan, Z. W.; Chen, M. R.; Wu, K.; Zhao, W. Z., (2+1)-Dimensional Integrable Heisenberg Supermagnet Model, J. Phys. Soc. Jpn, 81, 094006 (2012)
[21] Yan, Z. W.; Li, M. L.; Wu, K.; Zhao, W. Z., Integrable Deformations of Heisenberg Supermagnetic Model, Commun. Theor. Phys, 53, 21-24 (2010) · Zbl 1219.82215
[22] Yan, Z. W.; Li, M. L.; Wu, K.; Zhao, W. Z., Fermionic covariant prolongation structure theory for multidimensional super nonlinear evolution equation, J. Math. Phys, 54, 033506 (2013) · Zbl 1291.37100
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.