The Hamiltonian structure of a coupled system derived from a supersymmetric breaking of super Korteweg-de Vries equations. (English) Zbl 1284.81148
Summary: A supersymmetric breaking procedure for \(N = 1\) super Korteweg-de Vries (KdV), using a Clifford algebra, is implemented. Dirac’s method for the determination of constraints is used to obtain the Hamiltonian structure, via a Lagrangian, for the resulting solitonic system of coupled KdV type system. It is shown that the Hamiltonian obtained by this procedure is bounded from below and in that sense represents a model which is physically admissible.{
©2013 American Institute of Physics}
©2013 American Institute of Physics}
MSC:
| 81Q60 | Supersymmetry and quantum mechanics |
| 35Q53 | KdV equations (Korteweg-de Vries equations) |
| 35C08 | Soliton solutions |
| 81R40 | Symmetry breaking in quantum theory |
References:
| [1] | Ito, M., Phys. Lett. A, 91, 335-338 (1982) · doi:10.1016/0375-9601(82)90426-1 |
| [2] | Hirota, R.; Satsuma, J., Phys. Lett. A, 85, 407-408 (1981) · doi:10.1016/0375-9601(81)90423-0 |
| [3] | Yang, J.-R.; Mao, J.-J., Commun. Theor. Phys., 49, 22-26 (2008) · Zbl 1392.37059 · doi:10.1088/0253-6102/49/1/04 |
| [4] | Mogorosi, E. T.; Muatjetjeja, B.; Khalique, C. M., Boundary Value Probl., 150 (2012) · Zbl 1278.35199 · doi:10.1186/1687-2770-2012-150 |
| [5] | Wang, D. S., Appl. Math. Comp., 216, 1349-1354 (2010) · Zbl 1191.37036 · doi:10.1016/j.amc.2010.02.030 |
| [6] | Mathieu, P., J. Math. Phys., 29, 2499 (1988) · Zbl 0665.35076 · doi:10.1063/1.528090 |
| [7] | Labelle, P.; Mathieu, P., J. Math. Phys., 32, 923-927 (1991) · Zbl 0736.35100 · doi:10.1063/1.529351 |
| [8] | Miura, R. M.; Gardner, C. S.; Kruskal, M. D., J. Math. Phys., 9, 1204 (1968) · Zbl 0283.35019 · doi:10.1063/1.1664701 |
| [9] | Mathieu, P., Phys. Lett. B, 203, 287-291 (1988) · doi:10.1016/0370-2693(88)90554-0 |
| [10] | Dargis, P.; Mathieu, P., Phys. Lett. A, 176, 67-74 (1993) · doi:10.1016/0375-9601(93)90318-T |
| [11] | Andrea, S.; Restuccia, A.; Sotomayor, A., J. Math. Phys., 46, 103517 (2005) · Zbl 1111.37049 · doi:10.1063/1.2073289 |
| [12] | Andrea, S.; Restuccia, A.; Sotomayor, A., Phys. Lett. A, 376, 245-251 (2012) · Zbl 1255.81166 · doi:10.1016/j.physleta.2011.10.060 |
| [13] | Andrea, S.; Restuccia, A.; Sotomayor, A., J. Math. Phys., 42, 2625 (2001) · Zbl 1061.35102 · doi:10.1063/1.1368139 |
| [14] | Gao, X. N.; Lou, S. Y., Phys. Lett. B, 707, 209 (2012) · doi:10.1016/j.physletb.2011.12.021 |
| [15] | Gao, X. N.; Lou, S. Y.; Tang, X. Y., J. High Energy Phys., 5, 029 (2013) · Zbl 1342.81583 · doi:10.1007/JHEP05(2013)029 |
| [16] | Ren, B.; Lin, J.; Yu, J., Aip Advances, 3, 042129 (2013) · doi:10.1063/1.4802969 |
| [17] | Seiberg, N., J. High Energy Phys., 6, 010 (2003) · doi:10.1088/1126-6708/2003/06/010 |
| [18] | Dirac, P. A. M., Lectures on Quantum Mechanics, 2 (1964) · Zbl 0141.44603 |
| [19] | Nutku, Y., J. Math. Phys., 25, 6, 2007 (1984) · doi:10.1063/1.526395 |
| [20] | Kentwell, G. W., J. Math. Phys., 29, 46 (1988) · Zbl 0653.76010 · doi:10.1063/1.528133 |
| [21] | Gervais, J. L.; Neveau, A., Nucl. Phys. B, 209, 125 (1982) · doi:10.1016/0550-3213(82)90105-5 |
| [22] | Nam, S., Phys. Lett. B, 172, 323 (1986) · doi:10.1016/0370-2693(86)90261-3 |
| [23] | Benjamin, T. B., Proc. R. Soc. Lond. A, 328, 153-183 (1972) · doi:10.1098/rspa.1972.0074 |
| [24] | Bona, J., Proc. R. Soc. Lond. A, 344, 363-374 (1975) · Zbl 0328.76016 · doi:10.1098/rspa.1975.0106 |
| [25] | Olver, P. J.; Sokolov, V. V., Commun. Math. Phys., 193, 2, 245-268 (1998) · Zbl 0908.35124 · doi:10.1007/s002200050328 |
| [26] | Svinolupov, S. I.; Sokolov, V. V., Theor. Math. Phys. B, 100, 959-962 (1994) · Zbl 0875.35121 · doi:10.1007/BF01016758 |
| [27] | Foursov, M. V., J. Math. Phys., 44, 3088 (2003) · Zbl 1062.37068 · doi:10.1063/1.1580998 |
| [28] | Sotomayor, A.; Restuccia, A., J. Phys.: Conf. Ser., 410, 012073 (2013) · doi:10.1088/1742-6596/410/1/012073 |
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