Fermionic Covariant Prolongation Structure for a Super Nonlinear Evolution Equation in 2+1 Dimensions
Zhao-Wen Yan1** , Xiao-Li Wang2 , Min-Li Li3
1 School of Mathematical Sciences, Inner Mongolia University, Hohhot 0100212 School of Science, Qilu University of Technology, Ji'nan 2503533 School of Mathematical Sciences, Capital Normal University, Beijing 100048
Abstract ：The integrability of a (2+1)-dimensional super nonlinear evolution equation is analyzed in the framework of the fermionic covariant prolongation structure theory. We construct the prolongation structure of the multidimensional super integrable equation and investigate its Lax representation. Furthermore, the Bäcklund transformation is presented and we derive a solution to the super integrable equation.
收稿日期: 2017-04-14
出版日期: 2017-06-23
:
02.30.Ik
(Integrable systems)
02.30.Jr
(Partial differential equations)
02.40.-k
(Geometry, differential geometry, and topology)
[1] Mathieu P 1988 J. Math. Phys. 29 2499 [2] Bellucci S, Ivanov E, Krivonos S and Pichugin A 1993 Phys. Lett. B 312 463 [3] Manin Yu I and Radul A O 1985 Commun. Math. Phys. 98 65 [4] Roelofs G H M and Kersten P H M 1992 J. Math. Phys. 33 2185 [5] Popowicz Z 1994 Phys. Lett. A 194 375 [6] Makhankov V G and Pashaev O K 1992 J. Math. Phys. 33 2923 [7] Guo J F, Wang S K, Wu K, Yan Z W and Zhao W Z 2009 J. Math. Phys. 50 113502 [8] Yan Z W, Li M L, Wu K and Zhao W Z 2010 Commun. Theor. Phys. 53 21 [9] Saha M and Roy C A 1999 Int. J. Theor. Phys. 38 2037 [10] Yan Z W, Chen M R, Wu K and Zhao W Z 2012 J. Phys. Soc. Jpn. 81 094006 [11] Yan Z W 2017 Z. Naturforsch. A 72 331 [12] Liu Q P 1995 Lett. Math. Phys. 35 115 [13] Chaichian M and Kulish P P 1978 Phys. Lett. B 78 413 [14] Mathieu P 1988 Phys. Lett. A 128 169 [15] Ibort A, Martinez Alonso L and Reus E 1996 J. Math. Phys. 37 6157 [16] McArthur I N and Yung C M 1993 Mod. Phys. Lett. A 8 1739 [17] Ma W X, He J S and Qin Z Y 2008 J. Math. Phys. 49 033511 [18] Yu J, He J S, Ma W X and Cheng Y 2010 Chin. Ann. Math. B 31 361 [19] Wahlquist H D and Estabrook F B 1975 J. Math. Phys. 16 1 [20] Wang D S, Yin S J, Tian Y and Liu Y F 2014 Appl. Math. Comput. 229 296 [21] Wang D S and Wei X Q 2016 Appl. Math. Lett. 51 60 [22] Morris H C 1976 J. Math. Phys. 17 1870 [23] Morris H C 1977 J. Math. Phys. 18 285 [24] Lu Q K, Guo H Y and Wu K 1983 Commun. Theor. Phys. 2 1029 [25] Guo H Y, Hsiang Y Y and Wu K 1982 Commun. Theor. Phys. 1 495 [26] Cheng J P, Wang S K, Wu K and Zhao W Z 2010 J. Math. Phys. 51 093501 [27] Yan Z W, Li M L, Wu K and Zhao W Z 2013 J. Math. Phys. 54 033506 [28] Yang J Y and Ma W X 2016 Mod. Phys. Lett. B 30 1650381
[1]
.
[2]
.
[3]
.
[4]
.
[5]
.
[6]
.
[7]
.
[8]
.
[9]
.
[10]
.
[11]
.
[12]
.
[13]
.
[14]
.
[15]
.
2017, Vol. 34 
