Constructing super D-Kaup-Newell hierarchy and its nonlinear integrable coupling with self-consistent sources
Hanyu WEI1(), Tiecheng XIA2
1. College of Mathematics and Statistics, Zhoukou Normal University, Zhoukou 466001, China 2. Department of Mathematics, Shanghai University, Shanghai 200444, China
How to construct new super integrable equation hierarchy is an important problem. In this paper, a new Lax pair is proposed and the super D-Kaup-Newell hierarchy is generated, then a nonlinear integrable coupling of the super D-Kaup-Newell hierarchy is constructed. The super Hamiltonian structures of coupling equation hierarchy is derived with the aid of the super variational identity. Finally, the self-consistent sources of super integrable coupling hierarchy is established. It is indicated that this method is a straight- forward and efficient way to construct the super integrable equation hierarchy.
E S Afanasieva, V I Ryazanov, R R Salimov. On mappings in the Orlicz-Sobolev classes on Riemannian manifolds. J Math Sci, 2012, 181(1): 1–17 https://doi.org/10.1007/s10958-012-0672-z
X G Geng, W X Ma. A generalized Kaup-Newell spectral problem, soliton equations and finite-dimensional integrable systems. Nuov Cim A, 1995, 108(4): 477–486 https://doi.org/10.1007/BF02813604
W X Ma. A search for lump solutions to a combined fourth-order nonlinear PDE in (2+ 1)-dimensions. J Appl Anal Comput, 2019, 9: 1319–1332
12
W X Ma, M Chen. Hamiltonian and quasi-Hamiltonian structures associated with semi- direct sums of Lie algebras. J Phys A, 2006, 39(34): 10787–10801 https://doi.org/10.1088/0305-4470/39/34/013
13
W X Ma, J S He, Z Y Qin. A supertrace identity and its applications to super integrable systems. J Math Phys, 2008, 49(3): 033511 https://doi.org/10.1063/1.2897036
14
W X Ma, J Li, C M Khalique. A study on lump solutions to a generalized Hirota- Satsuma-Ito equation in (2+ 1)-dimensions. Complexity, 2018, 2018: 9059858 https://doi.org/10.1155/2018/9059858
15
W X Ma, J H Meng, M S Zhang. Nonlinear bi-integrable couplings with Hamiltonian structures. Math Comput Simulation, 2016, 127: 166–177 https://doi.org/10.1016/j.matcom.2013.11.007
16
W X Ma, Y Zhou. Lump solutions to nonlinear partial differential equations via Hirota bilinear forms. J Differential Equations, 2018, 264(4): 2633–2659 https://doi.org/10.1016/j.jde.2017.10.033
17
M McAnally, W X Ma. An integrable generalization of the D-Kaup-Newell soliton hierarchy and its bi-Hamiltonian reduced hierarchy. Appl Math Comput, 2018, 323: 220–227 https://doi.org/10.1016/j.amc.2017.11.004
G Z Tu. The trace identity, a powerful tool for constructing the Hamiltonian structure of integrable systems. J Math Phys, 1989, 30(2): 330–338 https://doi.org/10.1063/1.528449
20
G Z Tu. An extension of a theorem on gradients of conserved densities of integrable systems. Northeastern Math J, 1990, 6(1): 28–32
21
H Wang, T C Xia. Super Jaulent-Miodek hierarchy and its super Hamiltonian structure, conservation laws and its self-consistent sources. Front Math China, 2014, 9(6): 1367–1379 https://doi.org/10.1007/s11464-014-0419-x
22
H Y Wei, T C Xia. A new six-component super soliton hierarchy and its self-consistent sources and conservation laws. Chin Phys B, 2016, 25(1): 010201 https://doi.org/10.1088/1674-1056/25/1/010201
23
H Y Wei, T C Xia. Constructing variable coefficient nonlinear integrable coupling super AKNS hierarchy and its self-consistent sources. Math Methods Appl Sci, 2018, 41(16): 6883–6894 https://doi.org/10.1002/mma.5200
24
F J Yu. Nonautonomous rogue waves and ‘catch’ dynamics for the combined Hirota- LPD equation with variable coefficients. Commun Nonlinear Sci Numer Simul, 2016, 34: 142–153 https://doi.org/10.1016/j.cnsns.2015.10.018
Y F Zhang, L X Wu, W J Rui. A corresponding Lie algebra of a reductive homogeneous group and its applications. Commun Theor Phys (Beijing), 2015, 63(5): 535–548 https://doi.org/10.1088/0253-6102/63/5/535