| [1] |
Olver P J, Rosenau P. Tri-Hamiltonian duality between solitons and solitary-wave solutions having compact support. Physical Review E, 1996, 53(2):1900-1906
|
| [2] |
Wahlquist H D, Estabrook F B. Prolongation structures of nonlinear evolution equations. J Math Phys, 1975, 16(1):1-7
|
| [3] |
Estabrook F B, Wahlquist H D. Prolongation structures of nonlinear evolution equations Ⅱ. J Math Phys, 1976, 17(7):1293-1297
|
| [4] |
Roelofs G H M, Martini R. Prolongation structure of the KdV equation in the bilinear form of Hirota. Journal of Physics A:Mathematical and General, 1990, 23(11):1877-1884
|
| [5] |
Morris H C. Prolongation structures and nonlinear evolution equations in two spatial dimensions Ⅱ:A generalized nonlinear Schrödinger equation. J Math Phys, 1977, 18(2):285-288
|
| [6] |
Duan X J, Deng M, Zhao W Z, et al. The prolongation structure of the inhomogeneous equation of the reaction-diffusion type. Journal of Physics A:Mathematical and Theoretical, 2007, 40(14):3831-3837
|
| [7] |
Yang Y Q, Chen Y. Prolongation structure of the equation studied by Qiao. Communications in Theoretical Physics, 2011, 56(3):463-466
|
| [8] |
Wang D S, Ma Y Q, Li X G. Prolongation structures and matter-wave solitons in F=1 spinor BoseEinstein condensate with time-dependent atomic scattering lengths in an expulsive harmonic potential. Communications in Nonlinear Science and Numerical Simulation, 2014, 19(10):3556-3569
|
| [9] |
Bracken P. Exterior differential systems prolongations and application to a study of two nonlinear partial differential equations. Acta Appl Math, 2011, 113(3):247-263
|
| [10] |
Stalin S, Senthilvelan M. A note on the prolongation structure of the cubically nonlinear integrable Camassa-Holm type equation. Physics Letters A, 2011, 375(43):3786-3788
|
| [11] |
白永强, 裴明, 高文娟. Camassa-Holm和Degasperis-Procesi方程的延拓结构(英文). 河南大学学报(自然科学版), 2011, 41(6):551-555 Bai Y Q, Pei M, Gao W J. Prolongation structures of the Camassa-Holm and Degasperis-Procesi equations. Journal of Henan University (Natural Science), 2011, 41(6):551-555
|
| [12] |
Bracken P. An exterior differential system for a generalized Korteweg-de Vries equation and its associated integrability. Acta Appl Math, 2007, 95(3):223-231
|
| [13] |
Wang D S. Integrability of a coupled KdV system:Painlevé property, Lax pair and Bäcklund transformation. Applied Mathematics and Computation, 2010, 216(4):1349-1354
|
| [14] |
Wang D S. Complete integrability and the Miura transformation of a coupled KdV equation. Applied Mathematics Letters, 2010, 23(6):665-669
|
| [15] |
Cao Y H, Wang D S. Prolongation structures of a generalized coupled Korteweg-de Vries equation and Miura transformation. Communications in Nonlinear Science and Numerical Simulation, 2010, 15(9):2344-2349
|
| [16] |
Wang D S. Integrability of the coupled KdV equations derived from two-layer fluids:Prolongation structures and Miura transformations. Nonlinear Analysis:Theory, Methods and Applications, 2010, 73(1):270-281
|
| [17] |
Wang D S, Wei X Q. Integrability and exact solutions of a two-component Korteweg-de Vries system. Applied Mathematics Letters, 2016, 51:60-67
|
| [18] |
Wang D S, Liu J, Zhang Z F. Integrability and equivalence relationships of six integrable coupled Kortewegde Vries equations. Mathematical Methods in the Applied Sciences, 2016, 39(12):3516-3530
|
| [19] |
Humphreys J E. Introduction to Lie Algebras and Representation Theory. New York:Springer-Verlag, 1972
|
| [20] |
Jacobson N. Lie Algebras. New York:Dover Publications, 1979
|
| [21] |
Foursov M V. On integrable coupled KdV-type systems. Inverse Problems, 2000, 16(1):259-274
|
| [22] |
Flanders H. Differential Forms. New York:Academic Press, 1963:1-73
|
| [23] |
Dodd R, Fordy A P. The prolongation structures of quasi-polynomial flows. Proceedings of the Royal Society of London A:Mathematical, Physical and Engineering Sciences, The Royal Society, 1983, 385(1789):389-429
|
| [24] |
罗婷. 多分量KdV, mKdV方程组的对偶系统[D]. 西安:西北大学,2013 Luo T. Dual System of Multi-Component KdV and mKdV Equations[D]. Xi'an:Northwest Univesity, 2013
|
| [25] |
Fuchssteiner B. The Lie algebra structure of degenerate Hamiltonian and bi-Hamiltonian systems. Progress of Theoretical Physics, 1982, 68(4):1082-1104
|