-
1
-
-
0017901962
-
A numerical and theoretical study of certain nonlinear wave phenomena
-
B. Fornberg and G.B. Whitham, A numerical and theoretical study of certain nonlinear wave phenomena, Phil. Trans. R. Soc. Lond. A 289, 373-404, (1978).
-
(1978)
Phil. Trans. R. Soc. Lond. A
, vol.289
, pp. 373-404
-
-
Fornberg, B.1
Whitham, G.B.2
-
2
-
-
0000422597
-
Variational methods and applications to water waves
-
G.B. Whitham, Variational methods and applications to water waves, Proc. R. Soc. Lond. A 299, 6-25, (1967).
-
(1967)
Proc. R. Soc. Lond. A
, vol.299
, pp. 6-25
-
-
Whitham, G.B.1
-
4
-
-
12044253199
-
Compactons: Solitons with finite wavelength
-
P. Rosenau and J.M. Hyman, Compactons: Solitons with finite wavelength, Phys. Rev. Lett. 70, 564-567, (1993).
-
(1993)
Phys. Rev. Lett.
, vol.70
, pp. 564-567
-
-
Rosenau, P.1
Hyman, J.M.2
-
5
-
-
12044254491
-
An integrable shallow water equation with peaked solitons
-
R. Camassa and D.D. Holm, An integrable shallow water equation with peaked solitons, Phys. Rev. Lett. 71, 1661-1664, (1993).
-
(1993)
Phys. Rev. Lett.
, vol.71
, pp. 1661-1664
-
-
Camassa, R.1
Holm, D.D.2
-
6
-
-
56349110516
-
A new integrable shallow water equation
-
R. Camassa, D.D. Holm and J.M. Hyman, A new integrable shallow water equation, Adv. Appl. Mech. 31, 1-33, (1994).
-
(1994)
Adv. Appl. Mech.
, vol.31
, pp. 1-33
-
-
Camassa, R.1
Holm, D.D.2
Hyman, J.M.3
-
7
-
-
0001025045
-
The Lie algebra structure of a nonlinear evolution equations admitting infinite dimensional abelian symmetry groups
-
B. Fuchssteiner, The Lie algebra structure of a nonlinear evolution equations admitting infinite dimensional abelian symmetry groups, Progr. Theor. Phys. 65, 861-876, (1981).
-
(1981)
Progr. Theor. Phys.
, vol.65
, pp. 861-876
-
-
Fuchssteiner, B.1
-
8
-
-
49049150360
-
Symplectic structure, their Bäcklund transformations and hereditary symmetries
-
B. Fuchssteiner and A.S. Fokas, Symplectic structure, their Bäcklund transformations and hereditary symmetries, Physica D4 (47), (1981).
-
(1981)
Physica
, vol.D4
, Issue.47
-
-
Fuchssteiner, B.1
Fokas, A.S.2
-
9
-
-
0001662743
-
Solitons in the Camassa-Holm shallow water equation
-
F. Cooper and H. Shepard, Solitons in the Camassa-Holm shallow water equation, Phys. Lett. A194, 246-250, (1994).
-
(1994)
Phys. Lett.
, vol.A194
, pp. 246-250
-
-
Cooper, F.1
Shepard, H.2
-
11
-
-
0001702502
-
On a class of physically important integrable equations
-
A.S. Fokas, On a class of physically important integrable equations, Physica 87D, 145-150, (1994).
-
(1994)
Physica
, vol.87 D
, pp. 145-150
-
-
Fokas, A.S.1
-
13
-
-
22244482803
-
Some tricks from the symmetry-toolbox for nonlinear equations - Generalizations of the Camassa-Holm equation
-
B. Fuchssteiner, Some tricks from the symmetry-toolbox for nonlinear equations - generalizations of the Camassa-Holm equation, Physica 95D, 229-243, (1993).
-
(1993)
Physica
, vol.95 D
, pp. 229-243
-
-
Fuchssteiner, B.1
-
14
-
-
21844487106
-
Factorization and Painlevé analysis of a class of nonlinear third-order partial differential equations
-
C. Gilson and A. Pickering, Factorization and Painlevé analysis of a class of nonlinear third-order partial differential equations, J. Phys. A: Math. Gen. 28, 2871-2888, (1995).
-
(1995)
J. Phys. A: Math. Gen.
, vol.28
, pp. 2871-2888
-
-
Gilson, C.1
Pickering, A.2
-
16
-
-
0000582346
-
Tri-Hamiltonian soliton-compacton duality
-
P.J. Olver and P. Rosenau, Tri-Hamiltonian soliton-compacton duality, Phys. Rev E 53, 1900-1906, (1996).
-
(1996)
Phys. Rev E
, vol.53
, pp. 1900-1906
-
-
Olver, P.J.1
Rosenau, P.2
-
17
-
-
0001865962
-
Model equations for long waves in nonlinear dispersive systems
-
T.B. Benjamin, J.L. Bona and J. Mahoney, Model equations for long waves in nonlinear dispersive systems, Phil. Trans. R. Soc. Lond. Ser. A 272, 47-78, (1972).
-
(1972)
Phil. Trans. R. Soc. Lond. Ser. A
, vol.272
, pp. 47-78
-
-
Benjamin, T.B.1
Bona, J.L.2
Mahoney, J.3
-
18
-
-
84958444374
-
Calculations of the development of an undular bore
-
H. Peregrine, Calculations of the development of an undular bore, J. Fluid Mech. 25, 321-330, (1966).
-
(1966)
J. Fluid Mech.
, vol.25
, pp. 321-330
-
-
Peregrine, H.1
-
19
-
-
0041009474
-
The connection between partial differential equations soluble by inverse scattering and ordinary differential equations of Painlevé type
-
J.B. McLeod and P.J. Olver, The connection between partial differential equations soluble by inverse scattering and ordinary differential equations of Painlevé type, SIAM J. Math. Anal. 14, 488-506, (1983).
-
(1983)
SIAM J. Math. Anal.
, vol.14
, pp. 488-506
-
-
McLeod, J.B.1
Olver, P.J.2
-
20
-
-
0001803571
-
Dynamics of classical solitons
-
V.G. Makhankov, Dynamics of classical solitons, Phys. Rep. 35, 1-128, (1978).
-
(1978)
Phys. Rep.
, vol.35
, pp. 1-128
-
-
Makhankov, V.G.1
-
21
-
-
0028768164
-
Direct reduction and differential constraints
-
P.J. Olver, Direct reduction and differential constraints, Proc. R. Soc. Lond. A 444, 509-523, (1994).
-
(1994)
Proc. R. Soc. Lond. A
, vol.444
, pp. 509-523
-
-
Olver, P.J.1
-
22
-
-
36049057587
-
Method for solving the KdV equation
-
C.S. Gardner, J.M. Greene, M.D. Kruskal and R. Miura, Method for solving the KdV equation, Phys. Rev. Lett. 18, 1095-1097, (1967).
-
(1967)
Phys. Rev. Lett.
, vol.18
, pp. 1095-1097
-
-
Gardner, C.S.1
Greene, J.M.2
Kruskal, M.D.3
Miura, R.4
-
23
-
-
0016369301
-
The inverse scattering transform - Fourier analysis for nonlinear problems
-
M.J. Ablowitz, D.J. Kaup, A.C. Newell and H. Segur, The inverse scattering transform - Fourier analysis for nonlinear problems, Stud. Appl. Math. 53, 249-315, (1974).
-
(1974)
Stud. Appl. Math.
, vol.53
, pp. 249-315
-
-
Ablowitz, M.J.1
Kaup, D.J.2
Newell, A.C.3
Segur, H.4
-
24
-
-
56249128025
-
N-soliton solutions of model equations for shallow water waves
-
R. Hirota and J. Satsuma, N-soliton solutions of model equations for shallow water waves, J. Phys. Soc. Japan 40, 611-612, (1976).
-
(1976)
J. Phys. Soc. Japan
, vol.40
, pp. 611-612
-
-
Hirota, R.1
Satsuma, J.2
-
25
-
-
36749112076
-
The Painlevé property for partial differential equations
-
J. Weiss, M. Tabor and G. Carnevale, The Painlevé property for partial differential equations, J. Math. Phys. 24, 522-526, (1983).
-
(1983)
J. Math. Phys.
, vol.24
, pp. 522-526
-
-
Weiss, J.1
Tabor, M.2
Carnevale, G.3
-
26
-
-
51249180884
-
Nonlinear evolution equations and ordinary differential equaations of Painlevé type
-
M.J. Ablowitz, A. Ramani and H. Segur, Nonlinear evolution equations and ordinary differential equaations of Painlevé type, Phys. Rev. Lett. 23, 333-338, (1978).
-
(1978)
Phys. Rev. Lett.
, vol.23
, pp. 333-338
-
-
Ablowitz, M.J.1
Ramani, A.2
Segur, H.3
-
27
-
-
36749106124
-
A connection between nonlinear evolution equations and ordinary differential equations of P-type. I
-
M.J. Ablowitz, A. Ramani and H. Segur, A connection between nonlinear evolution equations and ordinary differential equations of P-type. I, J. Math. Phys. 21, 715-721, (1980).
-
(1980)
J. Math. Phys.
, vol.21
, pp. 715-721
-
-
Ablowitz, M.J.1
Ramani, A.2
Segur, H.3
-
28
-
-
35949021196
-
Painlevé conjecture revisited
-
A. Ramani, B. Dorizzi and B. Grammaticos, Painlevé conjecture revisited, Phys. Rev. Lett. 49, 539-1541, (1982).
-
(1982)
Phys. Rev. Lett.
, vol.49
, pp. 539-1541
-
-
Ramani, A.1
Dorizzi, B.2
Grammaticos, B.3
-
29
-
-
0343211316
-
The weak-Painlevé property as a criterion for the integrability of dynamical systems
-
A.F. Ranada, A. Ramani, B. Dorizzi and B. Grammaticos, The weak-Painlevé property as a criterion for the integrability of dynamical systems, J. Math. Phys. 26, 708-710, (1985).
-
(1985)
J. Math. Phys.
, vol.26
, pp. 708-710
-
-
Ranada, A.F.1
Ramani, A.2
Dorizzi, B.3
Grammaticos, B.4
-
30
-
-
0002247504
-
Review of symbolic software for the computation of Lie symmetries of differential equations
-
W. Hereman, Review of symbolic software for the computation of Lie symmetries of differential equations, Euromath. Bull. 1 (2), 45-79, (1994).
-
(1994)
Euromath. Bull.
, vol.1
, Issue.2
, pp. 45-79
-
-
Hereman, W.1
-
31
-
-
0026222880
-
The computer calculation of Lie point symmetries of large systems of differential equations
-
B. Champagne, W. Hereman and P. Winternitz, The computer calculation of Lie point symmetries of large systems of differential equations, Comp. Phys. Comm. 66, 319-340, (1991).
-
(1991)
Comp. Phys. Comm.
, vol.66
, pp. 319-340
-
-
Champagne, B.1
Hereman, W.2
Winternitz, P.3
-
32
-
-
0000478462
-
The general similarity of the heat equation
-
G.W. Bluman and J.D. Cole, The general similarity of the heat equation, J. Math. Mech. 18, 1025-1042, (1969).
-
(1969)
J. Math. Mech.
, vol.18
, pp. 1025-1042
-
-
Bluman, G.W.1
Cole, J.D.2
-
33
-
-
0013088734
-
Symmetries of compatibility conditions for systems of differential equations
-
E.M. Vorob'ev, Symmetries of compatibility conditions for systems of differential equations, Acta Appl. Math. 24, 1-24, (1991).
-
(1991)
Acta Appl. Math.
, vol.24
, pp. 1-24
-
-
Vorob'ev, E.M.1
-
34
-
-
0001678923
-
Nonclassical symmetry reduction: Example of the Boussinesq equation
-
D. Levi and P. Winternitz, Nonclassical symmetry reduction: Example of the Boussinesq equation, J. Phys. A: Math. Gen. 22, 2915-2924, (1989).
-
(1989)
J. Phys. A: Math. Gen.
, vol.22
, pp. 2915-2924
-
-
Levi, D.1
Winternitz, P.2
-
35
-
-
18944400520
-
New similarity solutions of the Boussinesq equation
-
P.A. Clarkson and M.D. Kruskal, New similarity solutions of the Boussinesq equation, J. Math. Phys. 30, 2201-2213, (1989).
-
(1989)
J. Math. Phys.
, vol.30
, pp. 2201-2213
-
-
Clarkson, P.A.1
Kruskal, M.D.2
-
36
-
-
33646984319
-
Nonclassical symmetry reductions of the Boussinesq equation
-
P.A. Clarkson, Nonclassical symmetry reductions of the boussinesq equation, Chaos, Solitons and Fractals 5, 2261-2301, (1989).
-
(1989)
Chaos, Solitons and Fractals
, vol.5
, pp. 2261-2301
-
-
Clarkson, P.A.1
-
37
-
-
0001870614
-
The nonclassical method is more general than the direct method for symmetry reductions: An example of the Fitzhugh-Nagumo equation
-
C. Nucci and P.A. Clarkson, The nonclassical method is more general than the direct method for symmetry reductions: An example of the Fitzhugh-Nagumo equation, Phys. Lett. A164, 49-56, (1992).
-
(1992)
Phys. Lett.
, vol.A164
, pp. 49-56
-
-
Nucci, C.1
Clarkson, P.A.2
-
38
-
-
21344479980
-
Nonclassical symmetry solutions and the methods of Bluman-Cole and Clarkson-Kruskal
-
D. Arrigo, P. Broadbridge and J.M. Hill, Nonclassical symmetry solutions and the methods of Bluman-Cole and Clarkson-Kruskal, J. Math. Phys. 34, 4692-4703, (1993).
-
(1993)
J. Math. Phys.
, vol.34
, pp. 4692-4703
-
-
Arrigo, D.1
Broadbridge, P.2
Hill, J.M.3
-
39
-
-
0001424046
-
Similarity reductions of partial differential equations
-
E. Pucci, Similarity reductions of partial differential equations, J. Phys. A: Math. Gen. 25, 2631-2640, (1992).
-
(1992)
J. Phys. A: Math. Gen.
, vol.25
, pp. 2631-2640
-
-
Pucci, E.1
-
40
-
-
84972500466
-
On new exact blow-up solutions for nonlinear heat conduction equations with source and applications
-
V.A. Galaktionov, On new exact blow-up solutions for nonlinear heat conduction equations with source and applications, Diff. Int. Eqns. 3, 863-874, (1990).
-
(1990)
Diff. Int. Eqns.
, vol.3
, pp. 863-874
-
-
Galaktionov, V.A.1
-
41
-
-
0000036454
-
Quasilinear heat equations with source: Blow-up, localization, symmetry, exact solutions, asymptotics, structures
-
V.A. Galaktionov, V.A. Dorodnytzin, G.G. Elenin, S.P. Kurdjumov and A.A. Samarskii, Quasilinear heat equations with source: Blow-up, localization, symmetry, exact solutions, asymptotics, structures, J. Sov. Math. 41, 1222-1292, (1988).
-
(1988)
J. Sov. Math.
, vol.41
, pp. 1222-1292
-
-
Galaktionov, V.A.1
Dorodnytzin, V.A.2
Elenin, G.G.3
Kurdjumov, S.P.4
Samarskii, A.A.5
-
42
-
-
0040378763
-
Optimal numerical algorithms
-
W.F. Ames, Optimal numerical algorithms, Appl. Num. Math. 10, 235-259, (1992).
-
(1992)
Appl. Num. Math.
, vol.10
, pp. 235-259
-
-
Ames, W.F.1
-
44
-
-
0343598076
-
Applications of the differential algebra package diffgrob2 to classical symmetries of differential equations
-
to appear
-
E.L. Mansfield and P.A. Clarkson, Applications of the differential algebra package diffgrob2 to classical symmetries of differential equations, J. Symb. Comp. (to appear), (1995).
-
(1995)
J. Symb. Comp.
-
-
Mansfield, E.L.1
Clarkson, P.A.2
-
45
-
-
43949149919
-
Symmetry reductions and exact solutions of a class of nonlinear heat equations
-
P.A. Clarkson and E.L. Mansfield, Symmetry reductions and exact solutions of a class of nonlinear heat equations, Physica D70, 250-288, (1994).
-
(1994)
Physica
, vol.D70
, pp. 250-288
-
-
Clarkson, P.A.1
Mansfield, E.L.2
-
47
-
-
0040816194
-
A triangularization algorithm which determines the Lie symmetry algebra of any system of PDEs
-
G.J. Reid, A triangularization algorithm which determines the Lie symmetry algebra of any system of PDEs, J. Phys. A: Math. Gen. 23, L853-L859, (1990).
-
(1990)
J. Phys. A: Math. Gen.
, vol.23
-
-
Reid, G.J.1
-
48
-
-
84972029082
-
Algorithms for reducing a system of PDEs to standard form, determining the dimension of its solution space and calculating its Taylor series solution
-
G.J. Reid, Algorithms for reducing a system of PDEs to standard form, determining the dimension of its solution space and calculating its Taylor series solution, Eur. J. Appl. Math. 2, 293-318, (1991).
-
(1991)
Eur. J. Appl. Math.
, vol.2
, pp. 293-318
-
-
Reid, G.J.1
-
50
-
-
0000174288
-
On a shallow water wave equation
-
P.A. Clarkson and E.L. Mansfield, On a shallow water wave equation, Nonlinearity 7, 975-1000, (1994).
-
(1994)
Nonlinearity
, vol.7
, pp. 975-1000
-
-
Clarkson, P.A.1
Mansfield, E.L.2
-
51
-
-
0028699959
-
Algorithms for the nonclassical method of symmetry reductions
-
P.A. Clarkson and E.L. Mansfield, Algorithms for the nonclassical method of symmetry reductions, SIAM J. Appl. Math. 54, 1693-1719, (1994).
-
(1994)
SIAM J. Appl. Math.
, vol.54
, pp. 1693-1719
-
-
Clarkson, P.A.1
Mansfield, E.L.2
-
52
-
-
0000233410
-
Symmetry reductions and exact solutions of shallow water wave equations
-
P.A. Clarkson and E.L. Mansfield, Symmetry reductions and exact solutions of shallow water wave equations, Acta Appl. Math. 39, 245-276, (1995).
-
(1995)
Acta Appl. Math.
, vol.39
, pp. 245-276
-
-
Clarkson, P.A.1
Mansfield, E.L.2
-
53
-
-
0003686926
-
-
Springer, New York
-
P.J. Olver, Applications of Lie Groups to Differential Equations, Second Edition, Graduate Texts Math., Volume 107, Springer, New York, (1993).
-
(1993)
Applications of Lie Groups to Differential Equations, Second Edition, Graduate Texts Math.
, vol.107
-
-
Olver, P.J.1
-
54
-
-
84972088211
-
New exact solutions for the Boussinesq equation
-
P.A. Clarkson, New exact solutions for the Boussinesq equation, Europ. J. Appl. Math. 1, 279-300, (1990).
-
(1990)
Europ. J. Appl. Math.
, vol.1
, pp. 279-300
-
-
Clarkson, P.A.1
-
55
-
-
24844461457
-
A note on the new similarity reductions of the Boussinesq equation
-
S.-Y. Lou, A note on the new similarity reductions of the Boussinesq equation, Phys. Lett. A151, 133-135, (1990).
-
(1990)
Phys. Lett.
, vol.A151
, pp. 133-135
-
-
Lou, S.-Y.1
-
56
-
-
43949163853
-
A perturbative Painlevé approach to nonlinear differential equations
-
R. Conte, A.P. Fordy and A. Pickering, A perturbative Painlevé approach to nonlinear differential equations, Physica D69, 33-58, (1993).
-
(1993)
Physica
, vol.D69
, pp. 33-58
-
-
Conte, R.1
Fordy, A.P.2
Pickering, A.3
-
57
-
-
0009920457
-
Hodograph transformations on lineraizable partial differential equations
-
P.A. Clarkson, A.S. Fokas and M.J. Ablowitz, Hodograph transformations on lineraizable partial differential equations, SIAM J. Appl. Math. 49, 1188-1209, (1989).
-
(1989)
SIAM J. Appl. Math.
, vol.49
, pp. 1188-1209
-
-
Clarkson, P.A.1
Fokas, A.S.2
Ablowitz, M.J.3
-
58
-
-
0002004721
-
Solitons, nonlinear evolution equations and inverse scattering
-
Cambridge University Press, Cambridge
-
M.J. Ablowitz and P.A. Clarkson, Solitons, nonlinear evolution equations and inverse scattering, In LMS Lecture Notes in Mathematics, Volume 149, Cambridge University Press, Cambridge, (1991).
-
(1991)
LMS Lecture Notes in Mathematics
, vol.149
-
-
Ablowitz, M.J.1
Clarkson, P.A.2
-
59
-
-
12044249264
-
Nonlinear dispersion and compact structures
-
P. Rosenau, Nonlinear dispersion and compact structures, Phys. Rev. Lett. 73, 1737-1741, (1993).
-
(1993)
Phys. Rev. Lett.
, vol.73
, pp. 1737-1741
-
-
Rosenau, P.1
|