Conservation laws and self-consistent sources for a super-HU equation hierarchy
-
摘要: 基于超矩阵李代数和超迹恒等式,建立了超HU方程族.然后又构造了超HU方程族的带有自相容源方程.最后通过引入两个变量F和G,获得了超HU方程族的无穷多个守恒律.Abstract: In the present paper, a super-HU hierarchy was constructed based on super-matrix Lie algebra and super-trace identity. In addition, an integrable super-HU equation hierarchy with self-consistent sources was established. Finally, we set up infinitely many conservation laws for an integrable super-HU equation hierarchy by introducing two variables F and G.
-
Key words:
- super-HU hierarchy /
- self-consistent sources /
- conservation laws
-
[1] HU X B. A powerful approach to generate new integrable systems[J]. Journal of Physics A:Mathematical and General, 1994, 27:2497-2514. doi: 10.1088/0305-4470/27/7/026 [2] HU X B. An approach to generate superextensions of integrable systems[J]. Journal of Physics A:Mathematical and General, 1997, 30:619-632. 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]. Journal of Mathematics Physics, 2008, 49:033511. doi: 10.1063/1.2897036 [4] WEI H Y, XIA T C. Nonlinear integrable couplings of super Kaup-Newell hierarchy and its super Hamiltonian structures[J]. Acta Physica Sinica, 2013, 62:13-20. http://d.old.wanfangdata.com.cn/Periodical/wlxb201312003 [5] TAO S X, XIA T C. Nonlinear super-integrable couplings of super Broer-Kaup-Kupershmidt Hierarchy and its super Hamiltonian structures[J]. Advances in Mathematica Physics, 2013:520765. http://www.ams.org/mathscinet-getitem?mr=3136832 [6] DONG H H, WANG X Z. Lie algebras and Lie super algebra for the integrable couplings of NLS-MKdV hierarchy[J]. Communications in Nonlinear Science and Numerical Simulation, 2009, 14:4071-4077. doi: 10.1016/j.cnsns.2009.03.010 [7] MEL'NIKOV V K. Intersection of the nonlinear schrodinger equation with a source[J]. Inverse Problems, 1992, 8:133-147. doi: 10.1088/0266-5611/8/1/009 [8] DOKTROV E V, VLASOV R A. Optical solitons in media with combined resonant and non-resonant (cubic) nonlinearities in the presence of perturbations[J]. Journal of Optics, 1991, 38:31-45. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=10.1080/09500349114550061 [9] MEL'NIKOV V K. Integration of the Korteweg-de Vries equation with a source[J]. Inverse Problems, 1990, 6:233-246. doi: 10.1088/0266-5611/6/2/007 [10] ZAKHAROV V E, KUZNETSOV E A. Multi-scale expansitions in the theory of systems integrable by the inverse scattering transform[J]. Physica D:Nonlinear phenomena, 1986, 18:455-463. doi: 10.1016/0167-2789(86)90214-9 [11] MEL'NIKOV V K. Integration of method of the Korteweg-de Vries equation with a self-consistent source[J]. Physics Letters A, 1988, 133:493-496. doi: 10.1016/0375-9601(88)90522-1 [12] LEON J. Solution of an initial-boundary value problem for coupled nonlinear waves[J]. Journal of Physics A:Mathematics and General, 1990, 23:1385-1403. doi: 10.1088/0305-4470/23/8/013 [13] LEON J. Spectral transform and solitons for generalized coupled Bloch systems[J]. Journal of Mathematical Physics, 1988, 29:2012-2019. doi: 10.1063/1.527859 [14] 胡贝贝, 张玲, 方芳. Li谱问题的超化及其自相容源[J].吉林大学学报(理学版), 2015, 53:229-234. http://d.old.wanfangdata.com.cn/Periodical/jldxzrkxxb201502014 [15] ZHANG D J. The N-soliton solutions of the MKdV equation with self-consistent sources[J]. Chaos, Solitons and Fractals, 2003, 18:31-43. doi: 10.1016/S0960-0779(02)00636-7 [16] ZENG Y B, MA W X, SHAO Y J. Two binary Darboux transformations for the KdV hierarchy with self-consistent sources[J]. Journal of Mathematical Physics, 2001, 42:2113-2128. doi: 10.1063/1.1357826 [17] ZENG Y B, SHAO Y J, MA W X. Integral-type darboux transformations for the mKdV hierarchy with selfconsistent sources[J]. Communications in theoretical Physics, 2002, 38:641-648. doi: 10.1088/0253-6102/38/6/641 [18] LI L. Conservation laws and self-consistent sources for a super-CKdV equation hierarchy[J]. Physics Lett A, 2011, 375:1402-1406. doi: 10.1016/j.physleta.2011.02.013 [19] WANG H, XIA T C. Conservation laws for a super G-J hierarchy with self-consistent sources[J]. Communications in Nonlinear Science and Numerical Simulation, 2012, 17:566-572. doi: 10.1016/j.cnsns.2011.06.007 [20] MIURA R M, GARDNER C S, KRUSKAL M D. Korteweg-de Vries equation and generalizations Ⅱ:Existence of conservation laws and constants of motion[J]. Journal of Mathematical Physics, 1968, 9:1204-1209. doi: 10.1063/1.1664701 [21] 胡贝贝, 张玲.超经典Boussinesq系统的守恒律和自相容源[J].数学杂志, 2016, 36:584-590. http://www.cnki.com.cn/Article/CJFDTOTAL-SXZZ201603016.htm [22] WANG H, XIA T C. Conservation laws and self-consistent sources for a super KN hierarchy[J]. Appl Math Comput, 2013, 219:5458-5464. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=7c13191fd5a4e8b54d474cdaf92225ae [23] LI L. Conservation laws and self-consistent sources for a super-CKdV equation hierarchy[J]. Physics Letters A, 2011, 375:1402-1406. doi: 10.1016/j.physleta.2011.02.013 [24] TAO S X. Self-Consistent sources and conservation laws for super coupled Burgers equation hierarchy[J]. International Journal of Applied Physics and Mathematics, 2013, 3:252-256. http://d.old.wanfangdata.com.cn/OAPaper/oai_doaj-articles_7c163b23f14194e9e5f45a8629741dfc [25] TU G Z. An extension of a theorem on gradients of conserved densities of integrable system[J]. Northeastern Math J, 1990, 6:26-32. https://www.researchgate.net/publication/243332910_The_Hamiltonian_structure_of_the_expanding_integrable_model_of_the_generalized_AKNS_hierarchy [26] ZHAI Y Y, GENG X G. Straightening out of the flows for the Hu hierarchy and its algebro-geometric solutions[J]. Math Anal Appl J, 2013, 397(2):561-576. doi: 10.1016/j.jmaa.2012.08.023
点击查看大图
计量
- 文章访问数: 128
- HTML全文浏览量: 39
- PDF下载量: 136
- 被引次数: 0