Lax pair, Bäcklund transformation and N-soliton-like solution for a variable-coefficient Gardner equation from nonlinear lattice, plasma physics and ocean dynamics with symbolic computation

Journal of Mathematical Analysis and Applications

Volumn 336, Issue 2, 2007, Pages 1443-1455

  Li, Juan ^a   Xu, Tao ^a   Meng, Xiang Hua ^a   Zhang, Ya Xing ^a   Zhang, Hai Qiang ^a   Tian, Bo ^a  

^a BEIJING UNIVERSITY OF POSTS AND TELECOMMUNICATIONS   (China)

Author keywords

Gardner equation; Integrable properties; Soliton solutions; Symbolic computation

Indexed keywords

EID: 34548087067     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2007.03.064     Document Type: Article

References (69)

1. Tian B., and Gao Y.T. Phys. Plasmas 12 (2005) 054701
2. Tian B., and Gao Y.T. Phys. Lett. A 340 (2005) 243
3. Tian B., and Gao Y.T. Phys. Lett. A 340 (2005) 449
4. Tian B., and Gao Y.T. Eur. Phys. J. D 33 (2005) 59
5. Tian B., and Gao Y.T. Phys. Plasmas (Lett.) 12 (2005) 070703
6. Gao Y.T., and Tian B. Phys. Lett. A 349 (2006) 314
7. Chudnovsky D., and Chudnovsky G. Proc. Natl. Acad. Sci. USA 96 (1999) 12263
8. Horii Z. Phys. Lett. A 306 (2002) 45
9. Horii Z. Phys. A 337 (2004) 398
10. Zhang L.P., and Xue J.K. Chaos Solitons Fractals 23 (2005) 543
11. Mason J., and Knobloch E. Phys. D 205 (2005) 100
12. Khater A.H., Abdallah A.A., El-Kalaawy O.H., and Callebaut D.K. Phys. Plasmas 6 (1999) 4542
13. Hirota R. J. Phys. Soc. Japan 33 (1972) 1456
14. Nejoh Y. Phys. Fluids B 4 (1992) 2830
15. Grimshaw R., Pelinovsky E., and Talipova T. Phys. D 132 (1999) 40
16. Gao Y.T., and Tian B. Phys. Plasmas (Lett.) 13 (2006) 120703
17. Wadati M. J. Phys. Soc. Japan 38 (1975) 673
18. Wadati M. J. Phys. Soc. Japan 38 (1975) 681
19. Mohamad M.N.B. Math. Methods Appl. Sci. 15 (1992) 73
20. Grimshaw R., Pelinovsky D., Pelinovsky E., and Slunyaev A. Chaos 12 (2002) 1070
21. Yu G.F., and Tam H.W. J. Math. Anal. Appl. 330 (2007) 989
22. Slyunyaev A.V. J. Exp. Theor. Phys. 92 (2001) 529
23. Chow K.W., Grimshaw R.H.J., and Ding E. Wave Motion 43 (2005) 158
24. Grimshaw R., Pelinovsky D., Pelinovsky E., and Talipova T. Phys. D 159 (2001) 35
25. Watanabe S. J. Phys. Soc. Japan 53 (1984) 950
26. Helfrich K.R., Melville W.K., and Miles J.W. J. Fluid Mech. 149 (1984) 305
27. Helfrich K.R., and Melville W.K. J. Fluid Mech. 167 (1986) 285
28. Han Q., Dai L.M., and Dong M.Z. Commun. Nonlinear Sci. Numer. Simul. 10 (2005) 607
29. Djordjevic V., and Redekopp L. J. Phys. Oceanogr. 8 (1978) 1016
30. Kakutani T., and Yamasaki N. J. Phys. Soc. Japan 45 (1978) 674
31. Miles J.W. Tellus 31 (1979) 456
32. Miles J.W. Tellus 33 (1981) 397
33. Holloway P.E., Pelinovsky E., Talipova T., and Barnes B. J. Phys. Oceanogr. 27 (1997) 871
34. Talipova T., Pelinovsky E., and Kouts T. Oceanology 38 (1998) 33
35. Gear J.A., and Grimshaw R. Phys. Fluids 26 (1983) 14
36. Lamb K.G., and Yan L. J. Phys. Oceanogr. 26 (1996) 2712
37. Malomed B.A., and Shrira V.I. Phys. D 53 (1991) 1
38. Hong W.P., and Yoon M.S. Z. Naturforsch. A 56 (2001) 366
39. Liu H.L., and Slemrod M. Appl. Math. Lett. 17 (2004) 401
40. Barnett M.P., Capitani J.F., Von Zur Gathen J., and Gerhard J. Int. J. Quantum Chem. 100 (2004) 80
41. Das G., and Sarma J. Phys. Plasmas 6 (1999) 4394
42. Yan Z.Y., and Zhang H.Q. J. Phys. A 34 (2001) 1785
43. Sirendaoreji. J. Phys. A 32 (1999) 6897
44. Ibrahim R. Chaos Solitons Fractals 16 (2003) 675
45. Hong W.P., and Park S.H. Int. J. Mod. Phys. C 15 (2004) 363
46. Xie F.D., and Gao X.S. Commun. Theor. Phys. 41 (2004) 353
47. Li B., Chen Y., Xuan H.N., and Zhang H.Q. Appl. Math. Comput. 152 (2004) 581
48. Tian B., and Gao Y.T. Phys. Lett. A 342 (2005) 228
49. Tian B., and Gao Y.T. Phys. Lett. A 359 (2006) 241
50. Gao Y.T., Tian B., and Zhang C.Y. Acta Mech. 182 (2006) 17
51. Tian B., Li H., and Gao Y.T. Z. Angew. Math. Phys. 56 (2005) 783
52. Joshi N. Phys. Lett. A 125 (1987) 456
53. Hlavatý L. Phys. Lett. A 128 (1988) 335
54. Clarkson P.A. IMA J. Appl. Math. 44 (1990) 27
55. Gazeau J.P., and Winternitz P. J. Math. Phys. 33 (1992) 4087
56. Tian B., Shan W.R., Zhang C.Y., Wei G.M., and Gao Y.T. Eur. Phys. J. B (Rapid Not.) 47 (2005) 329
57. Tian B., Wei G.M., Zhang C.Y., Shan W.R., and Gao Y.T. Phys. Lett. A 356 (2006) 8
58. Weiss J., Tabor M., and Carnevale G. J. Math. Phys. 24 (1983) 522
59. Zhang J.F. Int. J. Theor. Phys. 37 (1998) 1541
60. Yu J. Math. Methods Appl. Sci. 23 (2000) 1667
61. Hong W.P. Nuovo Cimento Soc. Ital. Fis. B 115 (2000) 117
62. Fu Z.T., Liu S.D., and Liu S.K. Chaos Solitons Fractals 20 (2004) 301
63. Yomba E. Phys. Lett. A 336 (2005) 463
64. Zhao X.Q., Zhi H.Y., Yu Y.X., and Zhang H.Q. Appl. Math. Comput. 172 (2006) 24
65. Li Y.S., and Zhang J.E. Chaos Solitons Fractals 16 (2003) 271
66. Zhang J.E., and Li Y.S. Phys. Rev. E 67 (2003) 016306
67. Li Y.S., Ma W.X., and Zhang J.E. Phys. Lett. A 275 (2000) 60
68. Dye J.M., and Parker A. J. Math. Phys. 42 (2001) 2567
69. Li Y.S., and Zhang J.E. Phys. Lett. A 284 (2001) 253