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1
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72149125297
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Variational identities and applications to Hamiltonian structures of soliton equations
-
doi:10.1016/j.na.2009.02.045
-
W.X. Ma, Variational identities and applications to Hamiltonian structures of soliton equations, Nonlinear Anal. 70 (2009), doi:10.1016/j.na.2009.02.045.
-
(2009)
Nonlinear Anal
, pp. 70
-
-
Ma, W.X.1
-
3
-
-
25444488023
-
The quadratic-form identity for constructing the Hamiltonian structure of integrable systems
-
F.K. Guo and Y.F. Zhang, The quadratic-form identity for constructing the Hamiltonian structure of integrable systems, J. Phys. A: Math. Gen. 38 (2005), pp. 8537-8548.
-
(2005)
J. Phys. A: Math. Gen
, vol.38
, pp. 8537-8548
-
-
Guo, F.K.1
Zhang, Y.F.2
-
4
-
-
33747173305
-
Hamiltonian and quasi-Hamiltonian structures associated with semi-direct sums of Lie algebras
-
W.X. Ma and M. Chen, Hamiltonian and quasi-Hamiltonian structures associated with semi-direct sums of Lie algebras, J. Phys. A: Math. Gen. 39 (2006), pp. 10787-10801
-
(2006)
J. Phys. A: Math. Gen
, vol.39
, pp. 10787-10801
-
-
Ma, W.X.1
Chen, M.2
-
5
-
-
36749037902
-
A discrete variational identity on semi-direct sums of Lie algebras
-
W.X. Ma, A discrete variational identity on semi-direct sums of Lie algebras, J. Phys. A: Math. Theor. 40 (2007), pp. 15055-15069.
-
(2007)
J. Phys. A: Math. Theor
, vol.40
, pp. 15055-15069
-
-
Ma, W.X.1
-
6
-
-
32144464619
-
Semi-direct sums of Lie algebras and continuous integrable couplings
-
W.X. Ma, X.X. Xu, and Y.F. Zhang, Semi-direct sums of Lie algebras and continuous integrable couplings, Phys. Lett. A 351 (2006), pp. 125-130.
-
(2006)
Phys. Lett. A
, vol.351
, pp. 125-130
-
-
Ma, W.X.1
Xu, X.X.2
Zhang, Y.F.3
-
7
-
-
33744767745
-
Semidirect sums of Lie algebras and discrete integrable couplings
-
W.X. Ma, X.X. Xu, and Y.F. Zhang, Semidirect sums of Lie algebras and discrete integrable couplings, J. Math. Phys. 47 (2006), pp. 053501-053516.
-
(2006)
J. Math. Phys
, vol.47
, pp. 053501-053516
-
-
Ma, W.X.1
Xu, X.X.2
Zhang, Y.F.3
-
8
-
-
0000913370
-
Integrable theory of the perturbation equations
-
W.X. Ma and B. Fuchssteiner, Integrable theory of the perturbation equations, Chaos Solitons Fractals 7 (1996), pp. 1227-1250.
-
(1996)
Chaos Solitons Fractals
, vol.7
, pp. 1227-1250
-
-
Ma, W.X.1
Fuchssteiner, B.2
-
9
-
-
0003043248
-
Integrable couplings of soliton equations by perturbations: I. A general theory and application to the KdV hierarchy
-
W.X. Ma, Integrable couplings of soliton equations by perturbations: I. A general theory and application to the KdV hierarchy, Methods Appl. Anal. 7 (2000), pp. 21-55.
-
(2000)
Methods Appl. Anal
, vol.7
, pp. 21-55
-
-
Ma, W.X.1
-
10
-
-
0003069487
-
The bi-Hamiltonian structure of the perturbation equations of the KdV hierarchy
-
W.X. Ma and B. Fuchssteiner, The bi-Hamiltonian structure of the perturbation equations of the KdV hierarchy, Phys. Lett. A 213 (1996), pp. 49-55.
-
(1996)
Phys. Lett. A
, vol.213
, pp. 49-55
-
-
Ma, W.X.1
Fuchssteiner, B.2
-
11
-
-
0345581675
-
A new loop algebra and a corresponding integrable hierarchy, as well as its integrable coupling
-
F.G. Guo and Y.F. Zhang, A new loop algebra and a corresponding integrable hierarchy, as well as its integrable coupling, J. Math. Phys. 44 (2003), pp. 5793-5803.
-
(2003)
J. Math. Phys
, vol.44
, pp. 5793-5803
-
-
Guo, F.G.1
Zhang, Y.F.2
-
12
-
-
4243131479
-
-
T.C. Xia, X.H. Chen, and D.Y. Chen, A new Lax integrable hierarchy N Hamiltonian structure and its integrable couplings system, Chaos Solitons Fractals 23 (2005), pp. 451-458.
-
(2005)
A New Lax Integrable Hierarchy N Hamiltonian Structure and Its Integrable Couplings System, Chaos Solitons Fractals
, vol.23
, pp. 451-458
-
-
Xia, T.C.1
Chen, X.H.2
Chen, D.Y.3
-
13
-
-
34248198455
-
Integrable couplings of the TC hierarchy and its Hamiltonian structure, Modern Phys
-
Z. Li, Y.J. Zhang, and H.H. Dong, Integrable couplings of the TC hierarchy and its Hamiltonian structure, Modern Phys. Lett. B 21 (2007), pp. 595-602.
-
(2007)
Lett. B
, vol.21
, pp. 595-602
-
-
Li, Z.1
Zhang, Y.J.2
Dong, H.H.3
-
14
-
-
39449113109
-
Hamiltonian structure of the integrable couplings for the multicomponent Dirac hierarchy
-
F.J. Yu and H.Q. Zhang, Hamiltonian structure of the integrable couplings for the multicomponent Dirac hierarchy, Appl. Math. Comput. 197 (2008), pp. 828-835.
-
(2008)
Appl. Math. Comput
, vol.197
, pp. 828-835
-
-
Yu, F.J.1
Zhang, H.Q.2
-
15
-
-
0035981865
-
A bi-Hamiltonian formulation for triangular systems by perturbations
-
W.X. Ma, A bi-Hamiltonian formulation for triangular systems by perturbations, J. Math. Phys. 43 (2002), pp. 1408-1421.
-
(2002)
J. Math. Phys
, vol.43
, pp. 1408-1421
-
-
Ma, W.X.1
-
16
-
-
51249184871
-
A hierarchy of Hamiltonian evolution equations associated with a generalized Schrödinger spectral problem
-
M. Boiti, P.J. Caudrey, and F. Pempinelli, A hierarchy of Hamiltonian evolution equations associated with a generalized Schrödinger spectral problem, Nuovo Cimento B 83 (1984), pp. 71-87.
-
(1984)
Nuovo Cimento B
, vol.83
, pp. 71-87
-
-
Boiti, M.1
Caudrey, P.J.2
Pempinelli, F.3
-
17
-
-
0041543760
-
Extending Hamiltonian operators to get bi-Hamiltonian coupled KdV systems
-
W.X. Ma and M. Pavlov, Extending Hamiltonian operators to get bi-Hamiltonian coupled KdV systems, Phys. Lett. A 246 (1998), pp. 511-522.
-
(1998)
Phys. Lett. A
, vol.246
, pp. 511-522
-
-
Ma, W.X.1
Pavlov, M.2
-
18
-
-
34447623208
-
A Hamiltonian structure associated with a matrix spectral problem of arbitrary- order
-
W.X. Ma, A Hamiltonian structure associated with a matrix spectral problem of arbitrary- order, Phys. Lett. A 367 (2007), pp. 473-477.
-
(2007)
Phys. Lett. A
, vol.367
, pp. 473-477
-
-
Ma, W.X.1
-
19
-
-
0004225382
-
-
World Scientific, Teaneck, NJ
-
A. Das, Integrable Models, World Scientific, Teaneck, NJ, 1989.
-
(1989)
Integrable Models
-
-
Das, A.1
-
20
-
-
36749108571
-
Evolution equations possessing infinitely many symmetries
-
P.J. Olver, Evolution equations possessing infinitely many symmetries, J. Math. Phys. 18 (1977), pp. 1212-1215.
-
(1977)
J. Math. Phys
, vol.18
, pp. 1212-1215
-
-
Olver, P.J.1
-
21
-
-
0001390841
-
Application of hereditary symmetries to nonlinear evolution equations
-
B. Fuchssteiner, Application of hereditary symmetries to nonlinear evolution equations, Nonlinear Anal. 3 (1979), pp. 849-862.
-
(1979)
Nonlinear Anal
, vol.3
, pp. 849-862
-
-
Fuchssteiner, B.1
-
22
-
-
0031127289
-
Review of symbolic software for Lie symmetry analysis: Algorithms and software for symbolic analysis of nonlinear systems
-
W. Hereman, Review of symbolic software for Lie symmetry analysis: Algorithms and software for symbolic analysis of nonlinear systems, Math. Comput. Model. 25 (1997), pp. 115-132.
-
(1997)
Math. Comput. Model
, vol.25
, pp. 115-132
-
-
Hereman, W.1
-
23
-
-
0031281728
-
Symbolic computation of conserved densities for systems of nonlinear evolution equations
-
U. Goktas and W. Hereman, Symbolic computation of conserved densities for systems of nonlinear evolution equations, J. Symbolic Comput. 24 (1997), pp. 591-621.
-
(1997)
J. Symbolic Comput
, vol.24
, pp. 591-621
-
-
Goktas, U.1
Hereman, W.2
-
24
-
-
36749117832
-
A simple model of the integrable Hamiltonian equation
-
F. Magri, A simple model of the integrable Hamiltonian equation, J. Math. Phys. 19 (1978), pp. 1156-1162.
-
(1978)
J. Math. Phys
, vol.19
, pp. 1156-1162
-
-
Magri, F.1
-
25
-
-
34249083504
-
Two unified formulae
-
F.K. Guo and Y.F. Zhang, Two unified formulae, Phys. Lett. A 366 (2007), pp. 403-410.
-
(2007)
Phys. Lett. A
, vol.366
, pp. 403-410
-
-
Guo, F.K.1
Zhang, Y.F.2
-
26
-
-
21844496963
-
New finite-dimensional integrable systems by symmetry constraint of the KdV equations
-
W.X. Ma, New finite-dimensional integrable systems by symmetry constraint of the KdV equations, J. Phys. Soc. Japan 64 (1995), pp. 1085-1091.
-
(1995)
J. Phys. Soc. Japan
, vol.64
, pp. 1085-1091
-
-
Ma, W.X.1
-
27
-
-
0040260844
-
On Liouville integrability of zero-curvature equations and the Yang hierarchy
-
G.Z. Tu, On Liouville integrability of zero-curvature equations and the Yang hierarchy, J. Phys. A: Math. Gen. 22 (1989), pp. 2375-2392.
-
(1989)
J. Phys. A: Math. Gen
, vol.22
, pp. 2375-2392
-
-
Tu, G.Z.1
-
28
-
-
0034708014
-
New completely integrable Neumann systems related to the perturbation KdV hierarchy
-
W.X. Ma and X.G. Geng, New completely integrable Neumann systems related to the perturbation KdV hierarchy, Phys. Lett. B 475 (2000), pp. 56-62.
-
(2000)
Phys. Lett. B
, vol.475
, pp. 56-62
-
-
Ma, W.X.1
Geng, X.G.2
-
29
-
-
0000684618
-
Complete integrability of the Korteweg-de Vries equation under perturbation around its solution: Lie Bäcklund symmetry approach
-
K.M. Tamizhmani and M. Lakshmanan, Complete integrability of the Korteweg-de Vries equation under perturbation around its solution: Lie Bäcklund symmetry approach, J. Phys. A: Math. Gen. 16 (1983), pp. 3773-3782.
-
(1983)
J. Phys. A: Math. Gen
, vol.16
, pp. 3773-3782
-
-
Tamizhmani, K.M.1
Lakshmanan, M.2
-
30
-
-
49049150360
-
Symplectic structures, their Bäcklund transformations and hereditary symmetries
-
B. Fuchssteiner and A.S. Fokas, Symplectic structures, their Bäcklund transformations and hereditary symmetries, Phys. D 4 82 (1981), pp. 47-66.
-
(1981)
Phys. D
, vol.4
, Issue.82
, pp. 47-66
-
-
Fuchssteiner, B.1
Fokas, A.S.2
-
31
-
-
49249093587
-
A new integrable generalization of the Korteweg-de Vries equation
-
A. Karasu-Kalkanli, A. Karasu, A. Sakovich, S. Sakovich, and R. Turhan, A new integrable generalization of the Korteweg-de Vries equation, J. Math. Phys. 49 (2008), pp. 073516-073526.
-
(2008)
J. Math. Phys
, vol.49
, pp. 073516-073526
-
-
Karasu-Kalkanli, A.1
Karasu, A.2
Sakovich, A.3
Sakovich, S.4
Turhan, R.5
-
32
-
-
17544403706
-
Enlarging spectral problems to construct integrable couplings of soliton equations
-
W.X. Ma, Enlarging spectral problems to construct integrable couplings of soliton equations, Phys. Lett. A 316 (2003), pp. 72-76.
-
(2003)
Phys. Lett. A
, vol.316
, pp. 72-76
-
-
Ma, W.X.1
-
33
-
-
0031515659
-
Lax representations and zero-curvature representations by the Kronecker product
-
W.X. Ma and F.K. Guo, Lax representations and zero-curvature representations by the Kronecker product, Int. J. Theor. Phys. 36 (1997), pp. 697-704.
-
(1997)
Int. J. Theor. Phys
, vol.36
, pp. 697-704
-
-
Ma, W.X.1
Guo, F.K.2
-
34
-
-
42749084735
-
A new method to construct the integrable coupling system for discrete soliton equation with the Kronecker product
-
F.J. Yu and L. Li, A new method to construct the integrable coupling system for discrete soliton equation with the Kronecker product, Phys. Lett. A 372 (2008), pp. 3548-3554.
-
(2008)
Phys. Lett. A
, vol.372
, pp. 3548-3554
-
-
Yu, F.J.1
Li, L.2
-
35
-
-
0037136277
-
Complexiton solutions to the Korteweg-de Vries equation
-
W.X. Ma, Complexiton solutions to the Korteweg-de Vries equation, Phys. Lett. A 301 (2002), pp. 35-44.
-
(2002)
Phys. Lett. A
, vol.301
, pp. 35-44
-
-
Ma, W.X.1
-
36
-
-
0344440950
-
Diversity of exact solutions to a restricted Boiti-Leon-Pempinelli dispersive long-wave system
-
W.X. Ma, Diversity of exact solutions to a restricted Boiti-Leon-Pempinelli dispersive long-wave system, Phys. Lett. A 319 (2003), pp. 325-333.
-
(2003)
Phys. Lett. A
, vol.319
, pp. 325-333
-
-
Ma, W.X.1
-
37
-
-
32544436100
-
Nonsingular positon and complexiton solutions for the coupled KdV system
-
H.C. Hu, B. Tong, and S.Y. Lou, Nonsingular positon and complexiton solutions for the coupled KdV system, Phys. Lett. A 351 (2006), pp. 403-412.
-
(2006)
Phys. Lett. A
, vol.351
, pp. 403-412
-
-
Hu, H.C.1
Tong, B.2
Lou, S.Y.3
-
38
-
-
33749021235
-
2D Toda lattice equation with self-consistent sources: Casoratian type solutions, bilinear Bäcklund transformation and Lax pair, in Special Issue: Topics on Integrable Systems
-
S.B. Damelin and W.X. Ma, eds
-
H.Y. Wang, X.B. Hu, and Gegenhasi, 2D Toda lattice equation with self-consistent sources: Casoratian type solutions, bilinear Bäcklund transformation and Lax pair, in Special Issue: Topics on Integrable Systems, S.B. Damelin and W.X. Ma, eds., pp. 133-143, 202 (2007), J. Comput. Appl. Math.
-
(2007)
J. Comput. Appl. Math
, pp. 133-143
-
-
Wang, H.Y.1
Hu, X.B.2
Gegenhasi3
-
39
-
-
34447624149
-
The exact solutions to the complex KdV equation
-
Y. Zhang, Y.N. Lv, L.Y. Ye, and H.Q. Zhao, The exact solutions to the complex KdV equation, Phys. Lett. A 367 (2007), pp. 465-472.
-
(2007)
Phys. Lett. A
, vol.367
, pp. 465-472
-
-
Zhang, Y.1
Lv, Y.N.2
Ye, L.Y.3
Zhao, H.Q.4
-
40
-
-
50949109194
-
An application of the Casoratian technique to the 2D Toda lattice equation
-
W.X. Ma, An application of the Casoratian technique to the 2D Toda lattice equation, Mod. Phys. Lett. B 22 (2008), pp. 1815-1825.
-
(2008)
Mod. Phys. Lett. B
, vol.22
, pp. 1815-1825
-
-
Ma, W.X.1
-
41
-
-
54849438541
-
The exact solution and integrable properties to the variable-coefficient modified Korteweg-de Vries equation
-
Y. Zhang, J.B. Li, and Y.N. Lv, The exact solution and integrable properties to the variable-coefficient modified Korteweg-de Vries equation, Ann. Physics 323 (2008), pp. 3059-3064.
-
(2008)
Ann. Physics
, vol.323
, pp. 3059-3064
-
-
Zhang, Y.1
Li, J.B.2
Lv, Y.N.3
-
42
-
-
68549092614
-
Exact one-periodic and two-periodic wave solutions to Hirota bilinear equations in 2+1 dimensions
-
W.X. Ma, R.G. Zhou, and L. Gao, Exact one-periodic and two-periodic wave solutions to Hirota bilinear equations in 2+1 dimensions, Mod. Phys. Lett. A 24 (2009), pp. 1677-1688.
-
(2009)
Mod. Phys. Lett. A
, vol.24
, pp. 1677-1688
-
-
Ma, W.X.1
Zhou, R.G.2
Gao, L.3
-
43
-
-
67650383727
-
A transformed rational function method and exact solutions to the 3+1 dimensional Jimbo-Miwa equation
-
W.X. Ma and J.H. Lee, A transformed rational function method and exact solutions to the 3+1 dimensional Jimbo-Miwa equation, Chaos Solitons Fractals, 42 (2009) 1356-1363.
-
(2009)
Chaos Solitons Fractals
, vol.42
, pp. 1356-1363
-
-
Ma, W.X.1
Lee, J.H.2
-
44
-
-
67749114336
-
Coupling integrable couplings
-
W.X. Ma and L. Gao, Coupling integrable couplings, Mod. Phys. Lett. B 23 (2009), pp. 1847-1860.
-
(2009)
Mod. Phys. Lett. B
, vol.23
, pp. 1847-1860
-
-
Ma, W.X.1
Gao, L.2
-
45
-
-
33748415728
-
Bihamiltonian equations on polynomial Virasoro algebras
-
P. Casati and G. Ortenzi, Bihamiltonian equations on polynomial Virasoro algebras, J. Nonlinear Math. Phys. 13 (2006), pp. 352-364.
-
(2006)
J. Nonlinear Math. Phys
, vol.13
, pp. 352-364
-
-
Casati, P.1
Ortenzi, G.2
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