一个新的可积广义超孤子族及其自相容源、守恒律

Abstract

Abstract:

Based on a Lie super algebra B(0, 1), a new generalized super soliton hierarchy is obtained. By making use of the super trace identity, the resulting super soliton hierarchy can be put into a super bi-Hamiltonian form. Then, the self-consistent sources of the generalized super soliton hierarchy is established. Furthermore, we present the infinitely many conservation laws for the integrable super soliton hierarchy.

Key words: Super trace identity, Super Hamiltonian structures, Self-consistent sources, Conservation laws

CLC Number:

O175.29

Hanyu Wei,Tiecheng Xia,Beibei Hu,Yan Zhang. A New Integrable Generalization of Super Soliton Hierarchy and Its Self-Consistent Sources and Conservation Laws[J].Acta mathematica scientia,Series A, 2020, 40(1): 187-199.

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References 36

1	Chowdhury A R , Roy S . On the Bäcklund transformation and Hamiltonian properties of superevaluation equations. J Math Phys, 1986, 27 (10): 2464- 2468 doi: 10.1063/1.527309
2	Hu X B . An approach to generate superextensions of integrable systems. J Phys A: Math Gen, 1997, 30 (2): 619- 632 doi: 10.1088/0305-4470/30/2/023
3	Ma W X , He J S , Qin Z Y . A supertrace identity and its applications to superintegrable systems. J Math Phys, 2008, 49 (3): 033511 doi: 10.1063/1.2897036
4	Ma W X. Nonlinear and Modern Mathematical Physics. New York: AIP Conference Proceedings, 2010
5	Yu F J , Feng L L , Li L . Darboux transformations for super-Schrödinger equation, super-Dirac equation and their exact solutions. Nonlinear Dynam, 2017, 88 (2): 1257- 1271
6	Yu F J , Li L . A new matrix Lie algebra, the multicomponent Yang hierarchy and its super-integrable coupling system. Appl Math Comput, 2009, 207 (2): 380- 387
7	Zhang Y F , Tam H W , Mei J Q . Some 2+1 dimensional super-integrable systems. Z Naturforsch, 2015, 70 (10): 791- 796 doi: 10.1515/zna-2015-0213
8	Tao S X , Xia T C . Lie algebra and Lie super algebra for integrable couplings of C-KdV hierarchy. Chin Phys Lett, 2010, 27 (4): 040202 doi: 10.1088/0256-307X/27/4/040202
9	Tao S X , Xia T C . Two super-integrable hierarchies and their super-Hamiltonian structures. Commun Nonlinear Sci Numer Simulat, 2011, 16 (1): 127- 132 doi: 10.1016/j.cnsns.2010.04.009
10	Yu J , Han W , He J S . Binary nonlinearization of the super AKNS system under an implicit symmetry constraint. J Phys A: Math Theor, 2009, 42 (46): 465201 doi: 10.1088/1751-8113/42/46/465201
11	Meŕnikov V K . Integration of the nonlinear Schrodinger equation with a source. Inverse Probl, 1992, 8 (1): 133- 147
12	Ma W X , Strampp W . An explicit symmetry constraint for the Lax pairs and the adjoint Lax pairs of AKNS systems. Phys Lett A, 1994, 185 (3): 277- 286 doi: 10.1016/0375-9601(94)90616-5
13	Yu F J , Li L . Integrable coupling system of JM equations hierarchy with self-consistent sources. Commun Theor Phys, 2010, 53 (1): 6- 12 doi: 10.1088/0253-6102/53/1/02
14	Yu F J . An integrable couplings of G-WKI equations hierarchy with self-consistent sources. Comput Math Appl, 2011, 61 (8): 2085- 2089 doi: 10.1016/j.camwa.2010.08.079
15	魏含玉, 夏铁成. 超Guo族的自相容源和守恒律. 数学物理学报, 2013, 33A (6): 1133- 1141
	Wei H Y , Xia T C . Conservation laws and self-consistent sources for a super-Guo equation hierarchy. Acta Math Sci (Ser A), 2013, 33A (6): 1133- 1141
16	Wang H , Xia T C . Super Jaulent-Miodek hierarchy and its super Hamiltonian structure, conservation laws and its self-consistent sources. Front Math China, 2014, 9 (6): 1367- 1379 doi: 10.1007/s11464-014-0419-x
17	Yu J , Ma W X , Han J W , Chen S T . An integrable generalization of the super AKNS hierarchy and its bi-Hamiltonian formulation. Commun Nonlinear Sci Numer Simulat, 2017, 43, 151- 157 doi: 10.1016/j.cnsns.2016.06.033
18	Miura R M , Gardner C S , Kruskal M D . Korteweg-de Vries equation and generalizations. I. A remarkable explicit nonlinear transformation. J Math Phys, 9 (8): 1204- 1209 doi: 10.1063/1.1664701
19	Wadati M , Sanuki H , Konno K . Relationships among inverse method, Bäcklund transformation and an infinite number of conservation laws. Progr Theoret Phys, 1975, 53 (2): 419- 436 doi: 10.1143/PTP.53.419
20	Ibragimov N H , Kolsrud T . Lagrangian approach to evolution equations: symmetries and conservation laws. Nonlinear Dyn, 2004, 36 (1): 29- 40
21	Yang J J , Ma W X . Conservation laws of a perturbed Kaup-Newell equation. Mod Phys Lett B, 2016, 30 (32): 1650381
22	Geng X G , Ma W X . A generalized Kaup-Newell spectral problem, soliton equations and finite-dimensional integrable systems. Il Nuovo Cimento A, 1995, 108 (4): 1965- 1970
23	Li Z , Dong H H , Yang H W . A super-soliton hierarchy and its super-Hamiltonian structure. Int J Theor Phys, 2009, 48 (7): 2172- 2176 doi: 10.1007/s10773-009-9995-z
24	Tu G Z . An extension of a theorem on gradients of conserved densities of integrable systems. Northeastern Math J, 1990, 6 (1): 28- 32
25	He J S , Yu J , Zhou R G . Binary nonlinearization of the super AKNS system. Mod Phys Lett B, 2008, 22 (4): 275- 288 doi: 10.1142/S0217984908014778
26	Tao S X , Wang H , Shi H . Binary nonlinearization of the super classical-Boussinesq hierarchy. Chin Phys B, 2011, 20 (7): 070201 doi: 10.1088/1674-1056/20/7/070201
27	Yu F J . Dynamics of nonautonomous discrete rogue wave solutions for an Ablowitz-Musslimani equation with PT-symmetric potential. Chaos, 2017, 27 (2): 023108 doi: 10.1063/1.4975763
28	Ma W X , Yong X L , Zhang H Q . Diversity of interaction solutions to the (2+1)-dimensional Ito equation. Comput Math Appl, 2018, 75 (1): 289- 295 doi: 10.1016/j.camwa.2017.09.013
29	Ma W X , Zhou Y . Lump solutions to nonlinear partial differential equations via Hirota bilinear forms. J Differ Equ, 264 (4): 2633- 2659 doi: 10.1016/j.jde.2017.10.033
30	Ma W X , Li J , Khalique C M . A study on lump solutions to a generalized Hirota-Satsuma-Ito equation in (2+1)-dimensions. Complexity, 2018, 2018, 9059858
31	Chen S T , Ma W X . Lump solutions of a generalized Calogero-Bogoyavlenskii-Schiff equation. Comput Math Appl, 2018, 76 (7): 1680- 1685 doi: 10.1016/j.camwa.2018.07.019
32	Ma W X . Abundant lumps and their interaction solutions of (3+1)-dimensional linear PDEs. J Geom Phys, 2018, 133, 10- 16 doi: 10.1016/j.geomphys.2018.07.003
33	Yang J J , Ma W X , Qin Z Y . Lump and lump-soliton solutions to the (2+1)-dimensional Ito equation. Anal Math Phys, 2018, 8 (3): 427- 436 doi: 10.1007/s13324-017-0181-9
34	Ma W X . Lump and interaction solutions of linear PDEs in (3+1)-dimensions. E Asian J Appl Math, 2019, 9 (1): 185- 194 doi: 10.4208/eajam.100218.300318
35	魏含玉, 夏铁成. 广义Broer-Kaup-Kupershmidt孤子方程的拟周期解. 数学物理学报, 2016, 36A (2): 317- 327
	Wei H Y , Xia T C . Quasi-periodic solution of the generalized Broer-Kaup-Kupershmidt soliton equation. Acta Math Sci (Ser A), 2016, 36A (2): 317- 327
36	孙玉娟, 丁琦, 梅建琴, 张鸿庆. D-AKNS方程的代数几何解. 数学物理学报, 2013, 33A (2): 276- 284 doi: 10.3969/j.issn.1003-3998.2013.02.011
	Sun Y J , Ding Q , Mei J Q , Zhang H Q . Algebro-Geometric solutions of the D-AKNS equations. Acta Math Sci (Ser A), 2013, 33A (2): 276- 284 doi: 10.3969/j.issn.1003-3998.2013.02.011

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A New Integrable Generalization of Super Soliton Hierarchy and Its Self-Consistent Sources and Conservation Laws

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