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Journal of Mathematical Physics

Volumn 30, Issue 10, 1989, Pages 2201-2213

New similarity reductions of the Boussinesq equation

(2) Clarkson, Peter A a Kruskal, Martin D b,c

a UNIVERSITY OF EXETER (United Kingdom)

b PRINCETON UNIVERSITY (United States)

c RUTGERS UNIVERSITY (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 18944400520 PISSN: 00222488 EISSN: None Source Type: Journal
DOI: 10.1063/1.528613 Document Type: Article

Times cited : (937)

References (88)

1
- 0001681902
- (1871) Comptes Rendus , vol.72 , pp. 755
- Boussinesq, J.¹

2
- 0001864672
- (1872) J. Math. Pures Appl. , vol.7 , pp. 55
- Boussinesq, J.¹

3
- 0001360283
- (1953) Proc. Camb. Philos. Soc. , vol.49 , pp. 685
- Ursell, F.¹

4
- 0001774896
- edited by W. F. Ames (Academic, New York)
- (1967) Nonlinear Partial Differential Equations , pp. 233-258
- Zabusky, N.J.¹

5
- 11744334220
- (1975) Phys. Rep. , vol.18 , pp. 1
- Toda, M.¹

6
- 0000060151
- (1974) Sov. Phys. JETP , vol.38 , pp. 108
- Zakharov, V.E.¹

7
- 0012743844
- edited by R. M. Miura (Springer, Berlin)
- (1975) Bäcklund Transformations, Lecture Notes in Mathematics , vol.515 , pp. 80-105
- Scott, A.C.¹

8
- 36749121906
- (1975) J. Math. Phys. , vol.16 , pp. 2301
- Ablowitz, M.J.¹ Haberman, R.²

9
- 84990633777
- (1980) Phys. Lett. A , vol.79 , pp. 264
- Caudrey, P.J.¹

10
- 0001811404
- (1982) Physica D , vol.6 , pp. 51
- Caudrey, P.J.¹

11
- 84990616652
- (1982) Commun. Pure Appl. Math. , vol.35 , pp. 567
- Deift, P.¹ Tomei, C.² Trubowitz, E.³

12
- 36049057587
- (1967) Phys. Rev. Lett. , vol.19 , pp. 1095
- Gardner, C.S.¹ Greene, J.M.² Kruskal, M.D.³ Miura, R.M.⁴

13
- 0003816609
- (SIAM, Philadelphia)
- (1981) Solitons and the Inverse Scattering Transform
- Ablowitz, M.J.¹ Segur, H.²

14
- 0003402370
- (North-Holland, Amsterdam)
- (1982) Spectral Transform and Solitons. I
- Calogero, F.¹ Degasperis, A.²

15
- 0003763749
- (Teuber, Leipzig, 1891) (reprinted by Chelsea, New York)
- (1967) Vorlesungen über Differentialgleichungen mit Bekannten Infinitesimalen Transformationen
- Lie, S.¹

16
- 0004065402
- (Springer, Berlin)
- (1974) Similarity Methods for Differential Equations, Applied Mathematical Sciences , vol.13
- Bluman, G.W.¹ Cole, J.D.²

17
- 0004171739
- (Academic, New York)
- (1982) Group Analysis of Differential Equations
- Ovsiannikov, L.V.¹

18
- 0003686926
- (Springer, New York)
- (1986) Applications of Lie Groups to Differential Equations, Graduate Texts in Mathematics , vol.107
- Olver, P.J.¹

19
- 0003229409
- edited by K. B. Wolf (Springer, Berlin)
- (1983) Nonlinear Phenomena, Lecture Notes in Physics , vol.189 , pp. 263-331
- Winternitz, P.¹

20
- 85034892045
- Courant Institute Report, COO-3077-160, MF-94
- (1979)
- Rosenau, P.¹ Schwarzmeier, J.²

21
- 84953817829
- preprint CRM-1278, Montreal
- (1985)
- Champagne, B.¹ Winternitz, P.²

22
- 0021869850
- (1985) Comput. , vol.34 , pp. 91
- Schwarz, F.¹

23
- 0024070164
- (1988) SIAM Rev. , vol.30 , pp. 450
- Schwarz, F.¹

24
- 0000478462
- (1969) J. Math. Mech. , vol.18 , pp. 1025
- Bluman, G.W.¹ Cole, J.D.²

25
- 46149142625
- (1986) Phys. Lett. A , vol.114 , pp. 107
- Olver, P.J.¹ Rosenau, P.²

26
- 0023327684
- (1987) SIAM J. Appl. Math. , vol.47 , pp. 263
- Olver, P.J.¹ Rosenau, P.²

27
- 0001504634
- (1918) Nachr. König. Gesell. Wissen Göttingen, Math. Phys. , vol.K1 , pp. 235
- Noether, E.¹

28
- 84930761411
- (1971) Transport Theory Stat. Phys. , vol.1 , pp. 186
- Noether, E.¹

29
- 2442432551
- (SIAM, Philadelphia)
- (1979) Lie-Bäcklund Transformations in Applications
- Anderson, R.L.¹ Ibragimov, N.H.²

30
- 0003689750
- (Reidel, Boston)
- (1985) Transformation Group Applied to Mathematical Physics
- Ibragimov, N.H.¹

31
- 36549097238
- (1988) J. Math. Phys. , vol.29 , pp. 806
- Bluman, G.W.¹ Kumei, S.² Reid, G.J.³

32
- 0001678923
- Since this was written, have provided such an explanation by showing all these similarity solutions of the Boussinesq equation can be obtained using the nonclassical method of Bluman and Cole.
- (1989) J. Phys. A: Math. Gen. , vol.22 , pp. 2915
- Levi, D.¹ Winternitz, P.²

33
- 0039381037
- (1982) Phys. Lett. A , vol.89 , pp. 379
- Nishitani, T.¹ Tajiri, M.²

34
- 5344252435
- (1986) Phys. Lett. A , vol.115 , pp. 75
- Rosenau, P.¹ Schwarzmeier, J.L.²

35
- 0004125699
- (Dover, New York)
- (1956) Ordinary Differential Equations
- Ince, E.L.¹

36
- 0000732496
- (1977) Phys. Rev. Lett. , vol.38 , pp. 1103
- Ablowitz, M.J.¹ Segur, H.²

37
- 51249180884
- (1978) Lett. Nuovo Cimento , vol.23 , pp. 333
- Ablowitz, M.J.¹ Ramani, A.² Segur, H.³

38
- 36749106124
- (1980) J. Math. Phys. , vol.21 , pp. 715
- Ablowitz, M.J.¹ Ramani, A.² Segur, H.³

39
- 0041009474
- (1983) SIAM J. Math. Anal. , vol.14 , pp. 488
- McLeod, J.B.¹ Olver, P.J.²

40
- 0039973258
- (1982) Phys. Lett. A , vol.91 , pp. 143
- Quispel, G.R.W.¹ Nijhoff, F.W.² Capel, H.W.³

41
- 0040052893
- (1981) Phys. Rev. Lett. , vol.47 , pp. 1096
- Fokas, A.S.¹ Ablowitz, M.J.²

42
- 36749114053
- (1982) J. Math. Phys. , vol.23 , pp. 2033
- Fokas, A.S.¹ Ablowitz, M.J.²

43
- 0003444747
- (Academic, New York)
- (1972) Nonlinear Partial Differential Equations in Engineering. Vol. II
- Ames, W.F.¹

44
- 0003748133
- (Pitman, London)
- (1982) Solutions of Differential Equations by Means of One-parameter Groups, Research Notes in Mathematics , vol.63
- Hill, J.M.¹

45
- 0004262752
- (Cambridge U.P., Cambridge,), 4th ed.
- (1927) Modern Analysis
- Whittaker, E.E.¹ Watson, G.M.²

46
- 0003464004
- edited by J. Moser (Springer, Berlin)310-354
- (1975) Dynamical Systems, Lecture Notes in Physics , vol.38
- Kruskal, M.D.¹

47
- 77950251516
- (1979) J. Phys. Soc. Jpn. , vol.47 , pp. 1698
- Wadati, M.¹ Konno, K.² Ichikawa, Y.H.³

48
- 0041018951
- (1984) Phys. Lett. A , vol.100 , pp. 7
- Levi, D.¹ Ragnisco, O.² Sym, A.³

49
- 0022060655
- (1985) J. Phys. Soc. Jpn. , vol.54 , pp. 2055
- Kawamoto, S.¹

50
- 0009920457
- (1989) SIAM J. Appl. Math. , vol.49 , pp. 1188
- Clarkson, P.A.¹ Fokas, A.S.² Ablowitz, M.J.³

51
- 0020333098
- (1982) J. Hydrol. , vol.56 , pp. 251
- Gilding, B.H.¹

52
- 0003614136
- (D. Reidel, Dordrecht)
- (1987) Symmetries of Maxwell’s Equations
- Fushchlich, W.I.¹ Nikitin, A.G.²

53
- 0010797446
- (1983) J. Phys. A: Math. Gen. , vol.16 , pp. 3645
- Fushchlich, W.I.¹ Serov, N.I.²

54
- 0007183127
- (1987) , vol.20 , pp. L929
- Fushchlich, W.I.¹ Serov, N.I.²

55
- 0002558667
- (1987) J. Phys. A: Math. Gen. , vol.20 , pp. L45
- Fushchlich, W.I.¹ Tsifra, I.M.²

56
- 23444459241
- (1988) J. Phys. A: Math. Gen. , vol.21 , pp. L5
- Fushchlich, W.I.¹ Zhdanov, R.Z.²

57
- 84980078224
- (1950) Commun. Pure Appl. Math. , vol.3 , pp. 201
- Hopf, E.¹

58
- 0000332692
- (1951) Quart. Appl. Math. , vol.9 , pp. 225
- Cole, J.D.¹

59
- 0347821899
- (1972) J. Phys. Soc. Jpn. , vol.32 , pp. 1681
- Wadati, M.¹

60
- 0016369301
- (1974) Stud. Appl. Math. , vol.53 , pp. 249
- Ablowitz, M.J.¹ Kaup, D.J.² Newell, A.C.³ Segur, H.⁴

61
- 0011643936
- (1987) J. Math. Phys. , vol.28 , pp. 1250
- Baumann, G.¹ Nonnenmacher, T.F.²

62
- 0002611736
- (1988) J. Math. Phys. , vol.29 , pp. 1
- Champagne, B.¹ Winternitz, P.²

63
- 0000794121
- (1986) J. Math. Phys. , vol.27 , pp. 1225
- David, D.¹ Kamran, N.² Levi, D.³ Winternitz, P.⁴

64
- 36549102806
- (1986) J. Math. Phys. , vol.27 , pp. 2848
- Dorizzi, B.¹ Grammaticos, B.² Ramani, A.³ Winternitz, P.⁴

65
- 0009050620
- (1988) J. Phys. A: Math. Gen. , vol.21 , pp. 1493
- Gagnon, L.¹ Winternitz, P.²

66
- 0042182371
- (1989) J. Phys. A , vol.22 , pp. 469
- Gagnon, L.¹ Winternitz, P.²

67
- 0007566683
- (1989) Phys. Rev. A , vol.39 , pp. 296
- Gagnon, L.¹ Winternitz, P.²

68
- 36549099541
- (1984) J. Math. Phys. , vol.25 , pp. 791
- Grundland, A.M.¹ Harnard, J.² Winternitz, P.³

69
- 0010798309
- (1987) J. Phys. A: Math. Gen. , vol.20 , pp. 6243
- Grundland, A.M.¹ Tuszyński, J.A.²

70
- 0010860157
- (1977) Phys. Lett. A , vol.119 , pp. 340
- Grundland, A.M.¹ Tuszyński, J.A.² Winternitz, P.³

71
- 0009132853
- (1986) J. Math. Phys. , vol.27 , pp. 2623
- Leo, R.A.¹ Martina, L.² Soliani, G.³

72
- 0041026562
- (1986) Prog. Theor. Phys. , vol.76 , pp. 739
- Leo, R.A.¹ Martina, L.² Soliani, G.³ Tondo, G.⁴

73
- 51649152467
- (1986) Nuovo Cimento B , vol.96 , pp. 89
- Leo, R.A.¹ Soliani, G.²

74
- 0346800381
- (1987) J. Math. Phys. , vol.28 , pp. 2317
- Matsuno, Y.¹

75
- 0001277015
- (1986) Phys. Lett. A , vol.118 , pp. 172
- Oron, A.¹ Rosenau, P.²

76
- 0348192745
- (1988) Phys. Lett. , vol.133 , pp. 213
- Skierski, M.¹ Grundland, A.M.² Tuszynski, J.A.³

77
- 36549092885
- (1987) J. Math. Phys. , vol.28 , pp. 2194
- Winternitz, P.¹ Grundland, A.M.² Tuszynski, J.A.³

78
- 0000099903
- (1988) J. Phys. C: Solid State Phys. , vol.21 , pp. 4931
- Winternitz, P.¹ Grundland, A.M.² Tuszynski, J.A.³

79
- 77952845886
- (1983) J. Phys. Soc. Jpn. , vol.52 , pp. 4059
- Kawamoto, S.¹

80
- 36749114221
- (1983) J. Math. Phys. , vol.24 , pp. 795
- Lakshmanan, M.¹ Kaliappan, P.²

81
- 0346593666
- (1982) J. Phys. Soc. Jpn. , vol.51 , pp. 1678
- Tajiri, M.¹ Kawamoto, S.²

82
- 36849110505
- (1968) J. Math. Phys. , vol.9 , pp. 1202
- Miura, R.M.¹

83
- 0040900507
- (1977) Prog. Theor. Phys. , vol.57 , pp. 797
- Hirota, R.¹ Satsuma, J.²

84
- 0001093688
- (1987) Differ. Eqs. , vol.23 , pp. 506
- Gromak, V.I.¹

85
- 27144447513
- (1988) Diff. Urav. , vol.23 , pp. 760
- Gromak, V.I.¹

86
- 0042173311
- (1911) Acta Math. , vol.34 , pp. 317
- Chazy, J.¹

87
- 0012853918
- (1983) Physica A , vol.117 , pp. 76
- Quispel, Q.R.W.¹ Capel, H.W.²

88
- 0010632367
- (1983) Math. Japon. , vol.28 , pp. 125
- Tajiri, M.¹ Kawamoto, S.² Thushima, K.³

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