Frontiers of Mathematics in China >
Constructing super D-Kaup-Newell hierarchy and its nonlinear integrable coupling with self-consistent sources
Received date: 24 May 2019
Accepted date: 26 Oct 2019
Published date: 15 Dec 2019
Copyright
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.
Hanyu WEI , Tiecheng XIA . Constructing super D-Kaup-Newell hierarchy and its nonlinear integrable coupling with self-consistent sources[J]. Frontiers of Mathematics in China, 2019 , 14(6) : 1353 -1366 . DOI: 10.1007/s11464-019-0802-8
| 1 |
Ablowitz M J, Fokas A S. Complex Variables: Introduction and Applications. Cambridge: Cambridge Univ Press, 2003
|
| 2 |
Afanasieva E S, Ryazanov V I, Salimov R R. On mappings in the Orlicz-Sobolev classes on Riemannian manifolds. J Math Sci, 2012, 181(1): 1–17
|
| 3 |
Fan E G, Zhang H Q. New exact solutions to a system of coupled KdV equations. Phys Lett A, 1998, 245(5): 389–392
|
| 4 |
Geng X G, Ma W X. A generalized Kaup-Newell spectral problem, soliton equations and finite-dimensional integrable systems. Nuov Cim A, 1995, 108(4): 477–486
|
| 5 |
Hu X B. An approach to generate superextensions of integrable systems. J Phys A, 1997, 30(2): 619–633
|
| 6 |
Ma W X. A new hierarchy of Liouville integrable generalized Hamiltonian equations and its reduction. Chinese J Contemp Math, 1992, 13(1): 79–89
|
| 7 |
Ma W X. Variational identities and Hamiltonian structures. AIP Conference Proceedings, 2010, 1212(1): 1–27
|
| 8 |
Ma W X. Nonlinear continuous integrable Hamiltonian couplings. Appl Math Comput, 2011, 217(17): 7238–7244
|
| 9 |
Ma W X. Integrable couplings and matrix loop algebras. AIP Conference Proceedings, 2013, 1562(1): 105–122
|
| 10 |
Ma W X. Interaction solutions to Hirota-Satsuma-Ito equation in (2+ 1)-dimensions. Front Math China, 2019, 14(3): 619–629
|
| 11 |
Ma W X. 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 |
Ma W X, Chen M. Hamiltonian and quasi-Hamiltonian structures associated with semi- direct sums of Lie algebras. J Phys A, 2006, 39(34): 10787–10801
|
| 13 |
Ma W X, He J S, Qin Z Y. A supertrace identity and its applications to super integrable systems. J Math Phys, 2008, 49(3): 033511
|
| 14 |
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
|
| 15 |
Ma W X, Meng J H, Zhang M S. Nonlinear bi-integrable couplings with Hamiltonian structures. Math Comput Simulation, 2016, 127: 166–177
|
| 16 |
Ma W X, Zhou Y. Lump solutions to nonlinear partial differential equations via Hirota bilinear forms. J Differential Equations, 2018, 264(4): 2633–2659
|
| 17 |
McAnally M, Ma W X. An integrable generalization of the D-Kaup-Newell soliton hierarchy and its bi-Hamiltonian reduced hierarchy. Appl Math Comput, 2018, 323: 220–227
|
| 18 |
Shchesnovich V S, Doktorov E V. Modified Manakov system with self-consistent source. Phys Lett A, 1996, 213(1): 23–31
|
| 19 |
Tu G Z. The trace identity, a powerful tool for constructing the Hamiltonian structure of integrable systems. J Math Phys, 1989, 30(2): 330–338
|
| 20 |
Tu G Z. An extension of a theorem on gradients of conserved densities of integrable systems. Northeastern Math J, 1990, 6(1): 28–32
|
| 21 |
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
|
| 22 |
Wei H Y, Xia T C. A new six-component super soliton hierarchy and its self-consistent sources and conservation laws. Chin Phys B, 2016, 25(1): 010201
|
| 23 |
Wei H Y, Xia T C. Constructing variable coefficient nonlinear integrable coupling super AKNS hierarchy and its self-consistent sources. Math Methods Appl Sci, 2018, 41(16): 6883–6894
|
| 24 |
Yu F J. Nonautonomous rogue waves and ‘catch’ dynamics for the combined Hirota- LPD equation with variable coefficients. Commun Nonlinear Sci Numer Simul, 2016, 34: 142–153
|
| 25 |
Zhang J F. Multiple soliton solutions of the dispersive long-wave equations. Chin Phys Lett, 1999, 16(1): 4–5
|
| 26 |
Zhang Y F, Wu L X, Rui W J. A corresponding Lie algebra of a reductive homogeneous group and its applications. Commun Theor Phys (Beijing), 2015, 63(5): 535–548
|
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