Inelastic interaction and non-traveling-wave effects for two multi-dimensional burgers models from fluid dynamics and astrophysics with symbolic computation

Zeitschrift fur Naturforschung - Section A Journal of Physical Sciences

Volumn 61, Issue 12, 2006, Pages 652-660

  Xu, Tao ^a   Zhang, Chun Yi ^b,c   Li, Juan ^a   Zhang, Hai Qiang ^a   Li, Li Li ^a   Tian, Bo ^a  

^a BEIJING UNIVERSITY OF POSTS AND TELECOMMUNICATIONS   (China)

^b Meteorology Center of Air Force Command Post   (China)

^c BEIHANG UNIVERSITY   (China)

Author keywords

Inelastic interaction; Multi dimensional burgers equations; N shock wave like solutions; Non traveling wave effects; Symbolic computation

Indexed keywords

EID: 33846398201     PISSN: 09320784     EISSN: None     Source Type: Journal    
DOI: 10.1515/zna-2006-1206     Document Type: Article

References (77)

1. J. Burgers, Adv. Appl. Mech. 1, 171 (1948).
2. M. J. Lighthill, Surveys in Mechanics (Eds. G. K. Batchelor and R. M. Davies), Cambridge University Press, Cambridge 1956.
3. E. A. Zabolotskaya and R. V. Khoklov, Sov. Phys. Acoust. 8, 35 (1969).
4. M. Bartuccelli, P. Pantano, and T. Brugarino, Lett. Nuov. Cim. 37, 433 (1983);
5. Bartuccelli, P. Carbonaro, and V. Muto, Lett. Nuov. Cim. 42, 279 (1985);
6. J. K. Hunter, SIAM J. Appl. Math. 48, 1 (1988).
7. R. A. Kraenkel, J. G. Pereira, and M. A. Manna, Phys. Rev. A 45, 838 (1992).
8. G. P. Zank and G. M. Webb, J. Plasma Phys. 44, 91 (1990).
9. G. Valenti, Wave Motion 12, 97 (1990).
10. H. Leblond and M. Manna, J. Phys. A 26, 6451 (1993).
11. G. M. Webb and G. P. Zank, J. Phys. A 23, 5465 (1990);
12. Phys. Lett. A 150, 14 (1990).
13. G. M. Webb and G. P. Zank, Astrophys. J. 396, 549 (1992).
14. H. Leblond, J. Phys. A 35, 10149 (2002).
15. H. Y. Ruan and Y. X. Chen, Phys. Rev. E 62, 5738 (2000);
16. A. R. Osborne, M. Onorato, M. Serio, and L. Bergamasco, Phys. Rev. Lett. 81, 3559 (1998);
17. Anastassiou, M. Segev, K. Steiglitz, J. A. Giordmaine, M. Mitchell, M. F. Shih, S. Lan, and J. Martin, Phys. Rev. Lett. 83, 2332 (1999);
18. Z. D. Li, L. Li, W. M. Liu, J. Q. Liang, and T. Ziman, Phys. Rev. E 68, 036102 (2003).
19. J. Hieterinta and R. Hirota, Phys. Lett. A 145, 237 (1990).
20. T. Soomere, Phys. Lett. A 332, 74 (2004);
21. T. Soomere and J. Engelbrecht, Eur. J. Mech. B-Fluid. 25, 636 (2006).
22. T. Kanna and M. Lakshmanan, Phys. Rev. Lett. 86, 5043 (2001);
23. T. Kanna, M. Lakshmanan, P. T. Dinda, and N. Akhmediev, Phys. Rev. E 73, 026604 (2006).
24. H. Hadouaj, B. A. Malomed, and G. A. Maugin, Phys. Rev. A 44, 3932 (1991).
25. C. L. Zheng and J. P. Fang, Z. Naturforsch. 61a, 16 (2006).
26. J. Pfeiffer, M. Schuster, A. A. Abdumalikov, and A. V. Ustinov, Phys. Rev. Lett. 96, 034103 (2006).
27. V. Tikhonenko, J. Christou, and B. Luther-Davies, Phys. Rev. Lett. 76, 2698 (1996).
28. A. Stepken, M. R. Belić, F. Kaiser, W. Królikowski, and B. Luther-Davies, Phys. Rev. Lett. 82, 540 (1999).
29. P. Pedri and L. Santos, Phys. Rev. Lett. 95, 200404 (2005).
30. Y. Murakami, J. Phys. Soc. Jpn. 59, 1 (1990);
31. S. Wang, X. Y. Tang, and S. Y. Lou, Chaos, Solitons and Fractals 21, 231 (2004).
32. F. Carbone, N. Aubry, J. Liu, J. P. Gollub, and R. Lima, Physica D 96, 182 (1996).
33. V. A. Gorodtsov, J. Exp. Theor. Phys. 89, 872 (1999).
34. E. Ben-Naim, S. Y. Chen, G. D. Doolen, and S. Redner, Phys. Rev. Lett. 83, 4069 (1999).
35. C. S. Chin, Phys. Rev. E 66, 021104 (2002).
36. Sirendaoreji, J. Phys. A 32, 6897 (1999);
37. J. Hietarinta, J. Phys. A 33, 5157 (2000).
38. Z. S. Lü and H. Q. Zhang, Appl. Math. Comput. 159, 401 (2004).
39. Z. S. Lü and H. Q. Zhang, Chaos, Solitons and Fractals 17, 669 (2003).
40. Z. Y. Yan, Phys. Lett. A 331, 193 (2004).
41. F. Güngör, J. Phys. A 34, 4313 (2001);
42. 35, 1805 (2002).
43. M. P. Barnett, J. F. Capitani, J. Von Zur Gathen, and J. Gerhard, Int. J. Quantum Chem. 100, 80 (2004);
44. G. Das and J. Sarma, Phys. Plasmas 6, 4394 (1999);
45. Z. Y. Yan and H. Q. Zhang, J. Phys. A 34, 1785 (2001);
46. W. P. Hong and S. H. Park, Int. J. Mod. Phys. C 15, 363 (2004);
47. F. D. Xie and X. S. Gao, Commun. Theor. Phys. 41, 353 (2004);
48. B. Tian and Y. T. Gao, Phys. Lett. A 340, 449 (2005);
49. 342, 228 (2005);
50. 359, 241 (2006); published online 2006, DOI:10.1016/jphysleta. 2006. 10.094;
51. Phys. Plasmas 12, 054701 (2005);
52. 12, 070703 (2005).
53. P. A. Clarkson and M. D. Kruskal, J. Math. Phys. 30, 2201 (1989).
54. E. Hopf, Commun. Pure Appl. Math. 3, 201 (1950);
55. J. D. Cole, Quart. Appl. Math. 9, 225 (1951);
56. E. R. Benton and G. W. Platzman, Quart. Appl. Math. 30, 195 (1972);
57. S. Hood, J. Math. Phys. 36, 1971 (1995);
58. Z. Qu, IMA J. Appl. Math. 54, 203 (1995);
59. W. P. Hong, Phys. Lett. A 268, 81 (2000).
60. S. Y. Lou, H. Y. Ruan, D. F. Chen, and W. Z. Chen, J. Phys. A 24, 1455 (1991);
61. H. D. Yu, Commun. Nonlinear Sci. Numer. Simul. 1, 28 (1996);
62. S. Y. Lou, X. Y. Tang, and J. Lin, J. Math. Phys. 41, 8286 (2000);
63. B. Tian and Y. T. Gao, Nuov. Cim. B 118, 175 (2003);
64. Z. Naturforsch. 59a, 997 (2004);
65. B. Tian, H. Li, and Y. T. Gao, Z. Angew. Math. Phys. 56, 783 (2005).
66. Y. T. Gao and B. Tian, Phys. Plasmas 13, 112901 (2006);
67. Phys. Plasmas (Lett.), in press 2006, AIP ID: 049612PHP;
68. Europhys. Lett., in press, 2006, REF: G18023/B10007;
69. Phys. Lett. A 349, 314 (2006);
70. Y. Chen, Z. Y. Yan, and H. Q. Zhang, Phys. Lett. A 307, 107 (2003);
71. Veerakumar and M. Daniel, Math. Comput. Simul. 62, 163 (2003).
72. Y. T. Gao, X. G. Xu, and B. Tian, Int. J. Mod. Phys. C 14, 1207 (2003).
73. R. A. Kraenkel, J. G. Pereira, and M. A. Manna, Phys. Rev. A 46, 4786 (1992);
74. P. M. Lushnikov, Phys. Lett. A 329, 49 (2004).
75. C. M. Ko, Adv. Space Res. 15, 149 (1995);
76. H. Kang and T. W. Jones, Astrophys. J. 620, 44 (2005).
77. M. J. Ablowitz and P. A. Clarkson, Solitons, Nonlinear Evolution Equations and Inverse Scattering, Cambridge University Press, Cambridge 1992.