×

Generalized fractional supertrace identity for Hamiltonian structure of NLS-MKdV hierarchy with self-consistent sources. (English) Zbl 1339.37051

Summary: In the paper, based on the modified Riemann-Liouville fractional derivative and Tu scheme, the fractional super NLS-MKdV hierarchy is derived, especially the self-consistent sources term is considered. Meanwhile, the generalized fractional supertrace identity is proposed, which is a beneficial supplement to the existing literature on integrable system. As an application, the super Hamiltonian structure of fractional super NLS-MKdV hierarchy is obtained.

MSC:

37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
35Q53 KdV equations (Korteweg-de Vries equations)
35R11 Fractional partial differential equations
17B80 Applications of Lie algebras and superalgebras to integrable systems
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Tu, GZ, The trace identity, a powerful tool for constructing the Hamiltonian structure of integrable systems, J. Math. Phys., 30, 330, (1989) · Zbl 0678.70015
[2] Tu, GZ, A trace identity and its application to the theory of discrete integrable systems, J. Phys. A: Math. Gen., 23, 3903, (1990) · Zbl 0717.58027
[3] Ma, WX, A new hierarchy of Liouville integrable generalized Hamiltonian equations and its reduction, Chin. J. Contemp. Math., 13, 79, (1992)
[4] Tu, GZ; Ma, WX, An algebraic approach for extending Hamiltonian operators, J. Partial Differ. Equ., 3, 53, (1992) · Zbl 0751.58016
[5] Hu, XB, A powerful approach to generate new integrable systems, J. Phys. A: Math. Gen., 27, 2497, (1994) · Zbl 0838.58018
[6] Guo, FK; Zhang, YF, The quadratic-form identity for constructing the Hamiltonian structure of integrable systems, J. Phys. A: Math. Gen., 38, 8537, (2005) · Zbl 1077.37045
[7] Li, Z; Zhang, YJ, A integrable system and its integrable coupling, J. Xinyang Norm. Univ. (Nat. Sci. Edition), 29, 493, (2009) · Zbl 1225.39012
[8] Guo, FK, A hierarchy of integrable Hamiltonian equations, Acta Math. Appl. Sin., 23, 181, (2000) · Zbl 1071.37514
[9] Dong, HH; Wang, XZ, Lie algebras and Lie super algebra for the integrable couplings of NLS-mkdv hierarchy, Commun. Nonlinear Sci. Numer. Simul., 14, 4071, (2009) · Zbl 1221.37120
[10] Ma, WX; Gao, L, Coupling integrable couplings, Mod. Phys. Lett. B, 23, 1847, (2009) · Zbl 1168.37320
[11] Ma, WX; He, JS; Qin, ZY, A supertrace identity and its applications to superintegrable systems, J. Math. Phys., 49, 033511, (2008) · Zbl 1153.81398
[12] Yu, FJ; Li, L, Integrable coupling system of JM equations hierarchy with self-consistent sources, J. Commun. Theor. Phys., 53, 6, (2010) · Zbl 1218.35197
[13] Yu, FJ, Non-isospectral integrable couplings of Ablowitz-Ladik hierarchy with self-consistent sources, J. Phys. Lett. A, 372, 6909, (2008) · Zbl 1227.37016
[14] Xia, TC, Two new integrable couplings of the soliton hierarchies with self-consistent sources, Chin. Phys. B., 19, 100303, (2010)
[15] Yang, HW; Dong, HH; Yin, BS; Liu, ZY, Nonlinear bi-integrable couplings of multi-component guo hierarchy with self-consistent sources, Adv. Math. Phys., 2012, 272904, (2012) · Zbl 1266.37035
[16] Zeng, YB; Ma, WX; Lin, RL, Integration of the soliton hierarchy with self-consistent sources, J. Math. Phys., 41, 5453, (2000) · Zbl 0968.37023
[17] Yang, HW; Yin, BS; Shi, YL, Forced dissipative Boussinesq equation for solitary waves excited by unstable topography, Nonlinear Dyn., 70, 1389, (2012)
[18] Yang, HW; Wang, XR; Yin, BS, A kind of new algebraic Rossby solitary waves generated by periodic external source, Nonlinear Dyn., 76, 1725, (2014) · Zbl 1314.76019
[19] Caputo, M, Linear model of dissipation whose Q is almost frequency dependent II, Geophys. J. R. Astron. Soc., 13, 529, (1967)
[20] Djrbashian, MM; Nersesian, AB, Fractional derivative and the Cauchy problem for differential equations of fractional order (in Russian), Izv. Aead. Nauk Armjanskoi SSR., 3, 3, (1968)
[21] Hu, XB, An approach to generate superextensions of integrable systems, J. Phys. A: Math. Gen., 30, 619, (1997) · Zbl 0947.37039
[22] Kupershmidt, BA, Mathematics of dispersive water waves, Commun. Math. Phys., 99, 51, (1985) · Zbl 1093.37511
[23] Guo, FK; Zhang, YF, A type of new loop algebra and a generalized Tu formula, Commum. Theor. Phys., 51, 39, (2009) · Zbl 1175.81126
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.