On the integrability of a generalized variable-coefficient KadomtsevPetviashvili equation

Journal of Physics A: Mathematical and Theoretical

Volumn 45, Issue 5, 2012, Pages

  Tian, Shou Fu ^a,b   Zhang, Hong Qing ^a  

^a DALIAN UNIVERSITY OF TECHNOLOGY   (China)

^b UNIVERSITY OF BRITISH COLUMBIA   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84863031091     PISSN: 17518113     EISSN: 17518121     Source Type: Journal    
DOI: 10.1088/1751-8113/45/5/055203     Document Type: Article

References (88)

1. Ablowitz M J and Clarkson P A 1991 Solitons, Nonlinear Evolution Equations and Inverse Scattering (New York: Cambridge University Press)
2. Wadati M, Konno K and Ichikawa Y H 1979 J. Phys. Soc. Japan 46 1965
3. Matveev V B and Salle M A 1991 Darboux Transformation and Solitons (Berlin: Springer)
4. Dubrousky V G and Konopelchenko B G 1994 J. Phys. A: Math. Gen. 27 4619
5. Wadati M 1975 J. Phys. Soc. Japan 38 673
6. Wadati M, Sanuki H and Konno K 1975 Prog. Theor. Phys. 53 419
7. Hirota R 1991 The Direct Method in Soliton Theory (New York: Cambridge University Press)
8. Matsuno Y 1984 Bilinear Transformation Method (New York: Academic)
9. Hu X B and Clarkson P A 1995 J. Phys. A: Math. Gen. 28 5009
10. Hu X B, Li C X, Nimmo J J C and Yu G F 2005 J. Phys. A: Math. Gen. 38 195
11. Zhang D J and Chen D Y 2003 J. Phys. Soc. Japan 72 448
12. Zhang D J 2002 J. Phys. Soc. Japan 71 2649
13. Ma W X and You Y C 2005 Trans. Am. Math. Soc. 357 1753
14. Bell E T 1834 Ann. Math. 35 258
15. Gilson C, Lambert F, Nimmo J and Willox R 1996 Proc. R. Soc. A 452 223
16. Lambert F, Loris I and Springael J 2001 Inverse Problems 17 1067
17. Lambert F and Springael J 2008 Acta Appl. Math. 102 147
18. Abramowitz M and Stegun J A (ed) 1972 Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables (New York: Dover)
19. Riordan J 1996 Combinatorial Identities (New York: Wiley)
20. Comtet L 1974 Advanced Combinatorics (Dordrecht: Reidel)
21. Howard F T 1980 Math. Comput. 35 977
22. Noschese S and Ricci P E 2003 J. Comput. Anal. Appl. 5 333
23. Bernardini A, Natalini P and Ricci P E 2005 Comput. Math. Appl. 50 1697
24. Paris R B 2009 J. Comput. Appl. Math. 232 216
25. Coffey M 1996 Phys. Rev. B 54 1279
26. Das G and Sarma J 1999 Phys. Plasmas 6 4394
27. Tian B, Shan W R, Zhang C Y, Wei G M and Gao Y T 2005 Eur. Phys. J. B 47 329
28. Anders I and Boutet de Monvel A 2000 J. Nonlinear Math. Phys. 7 284
29. Shen S F, Zhang J, Ye C E and Pan Z L 2005 Phys. Lett. A 337 101
30. Fan E G 2000 J. Phys. A: Math. Gen. 33 6925 (arXiv:1008.4194v1)
31. Yan Z Y and Zhang H Q 2001 J. Phys. A: Math. Gen. 34 1785
32. Dai C Q and Zhang J F 2006 J. Phys. A: Math. Gen. 39 723
33. Zhang J F, Zhu Y J and Lin J 1995 Commun. Theor. Phys. 24 69
34. Wang Q and Cheng Y 2006 Appl. Math. Comput. 181 48
35. David D, Levi D and Winternitz P 1987 Stud. Appl. Math. 76 133
36. David D, Levi D and Winternitz P 1986 Phys. Lett. A 118 390
37. Levi D and Winternitz P 1988 Phys. Lett. A 129 165
38. Clarkson P A 1990 IMA J. Appl. Math. 44 27
39. Oevel W and Steeb W H 1984 Phys. Lett. A 103 239
40. Gngr F and Winternitz P 2002 J. Math. Anal. Appl. 276 314
41. Lou S Y and Tang X Y 2004 J. Math. Phys. 45 1020
42. Chen Y and Liu P L-F 1995 J. Fluid Mech. 288 383
43. Apel J R, Ostrovsky L A, Stepanyants Y A and Lynch J F 2007 J. Acoust. Soc. Am. 121 695
44. Lax P D 1968 Commun. Pure Appl. Math. 21 467
45. Kruskal M D, Miura R M, Gardner C S and Zabusky N J 1970 J. Math. Phys. 11 952
46. Kadomtsev B B and Petviashvili V I 1970 Sov. Phys. Dokl. 15 539
47. Bryant P J 1982 J. Fluid Mech. 115 525
48. Lin M M and Duan W S 2005 Chaos Solitons Fractals 23 929
49. Wazwaz A M 2007 Appl. Math. Comput. 190 633
50. Maxon S and Viecelli J 1974 Phys. Fluids 17 1614
51. Hlavaty V 1986 J. Phys. Soc. Japan 55 1405
52. Tian B and Gao Y T 2005 Phys. Lett. A 340 449
53. Li J, Zhang H Q, Xu T, Zhang Y X, Hu W and Tian B 2007 J. Phys. A: Math. Theor. 40 7643
54. Johnson R 1980 J. Fluid. Mech. 97 701
55. Johnson R S 1997 A Modern Introduction to the Mathematical Theory of Water Waves (Cambridge: Cambridge University Press)
56. Nakamura A 1988 Prog. Theor. Phys. Suppl. 94 195
57. Li J B and Zhang Y 2009 Nonlinear Anal.: Real World Appl. 10 2502
58. Yan Z Y and Zhang H Q 2000 Appl. Math. Mech. 21 645
59. Zhu Z N 1992 Acta Phys. Sin. 41 1561 (in Chinese)
60. Zhu Z N 1993 Phys. Lett. A 182 277
61. Hon Y C and Fan E G 2011 IMA J. Appl. Math. in press
62. Cao C W, Wu Y T and Geng X G 1999 J. Math. Phys. 40 3948
63. Lou S Y and Hu X B 1997 J. Math. Phys. 38 6401
64. Deng S F and Qin Z Y 2006 Phys. Lett. A 357 467
65. Fan E G and Hon Y C 2008 Phys. Rev. E 78 036607
66. Fan E G and Hon Y C 2010 Phys. Lett. A 374 3629
67. Ma W X, Zhou R G and Gao L 2009 Mod. Phys. Lett. A 21 1677
68. Zhou R G and Ma W X 2000 Appl. Math. Lett. 13 131
69. He J S, Li Y S and Cheng Y 2003 J. Math. Phys. 44 3928
70. Dai H H and Li Y S 2005 J. Phys. A: Math. Gen. 38 L685
71. Zhou Z X 1996 Inverse Problems 12 89
72. Zeng Y B, Shao Y J and Xue W M 2003 J. Phys. A: Math. Gen. 36 5035
73. Li Z B and Wang M L 1993 J. Phys. A: Math. Gen. 26 6027
74. Geng X G and Cao C W 2004 Chaos Solitons Fractals 22 683
75. Xia T C and Fan E G 2005 J. Math. Phys. 46 043510
76. Yan Z Y and Zhang H Q 2002 J. Math. Phys. 43 4978
77. Yu G F and Tam H W 2006 J. Phys. A: Math. Gen. 39 3367
78. Qu C Z and Shen S F 2009 J. Math. Phys. 50 103522
79. Qiao Z J, Cao C W and Strampp W 2003 J. Math. Phys. 44 701
80. Zhang Y F and Zhang H Q 2002 J. Math. Phys. 43 466
81. Wang D S and Zhang Z F 2009 J. Phys. A: Math. Theor. 42 035209
82. Weiss J, Tabor M and Carnevale G 1983 J. Math. Phys. 24 522
83. Tian S F, Wang Z and Zhang H Q 2010 J. Math. Anal. Appl. 366 646
84. Tian S F and Zhang H Q 2010 J. Nonlinear Math. Phys. 17 491
85. Hereman W and Zhuang W 1995 Acta Appl. Math. 39 361
86. Hirota R, Hu X B and Tang X Y 2003 J. Math. Anal. Appl. 288 326
87. Tian S F and Zhang H Q 2010 J. Math. Anal. Appl. 371 585
88. Tian S F and Zhang H Q 2011 Commun. Nonlinear Sci. Numer. Simul. 16 173