Approximate similarity reduction for singularly perturbed Boussinesq equation via symmetry perturbation and direct method

Journal of Mathematical Physics

Volumn 49, Issue 9, 2008, Pages

  Jiao, Xiaoyu ^a   Yao, Ruoxia ^a,b,c   Lou, S Y ^a,b  

^a SHANGHAI JIAO TONG UNIVERSITY   (China)

^b NINGBO UNIVERSITY   (China)

^c SHAANXI NORMAL UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 54749112730     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.2976034     Document Type: Article

References (28)

1. S. Lie, Vorlesungen über Differentialgleichungen mit Bekannten Infinitesimalen Transformationen (Teuber, Leipzig, 1891) (reprinted by Chelsea, New York, 1967).
2. G. W. Bluman and J. D. Cole, Similarity Methods for Differential Equations, Applied Mathematical Sciences Vol. 13 (Springer, Berlin, 1974).
3. G. W. Bluman and S. Kumei, Symmetries and Differential Equations, Applied Mathematical Sciences Vol. 81 (Springer-Verlag, Berlin, 1989).
4. L. V. Ovisiannikov, Group Analysis of Differential Equations (Academic, New York, 1982).
5. P. J. Olver, Applications of Lie Groups to Differential Equations, Graduate Texts in Mathematics, 2nd ed. (Springer-Verlag, New York, 1993).
6. P. Winternitz, in Nonlinear Phenomena, Lecture Notes in Physics Vol. 189 edited by, K. B. Wolf, (Springer, Berlin, 1983), pp. 263-305.
7. G. W. Bluman and J. D. Cole, J. Math. Mech. 18, 1025 (1969).
8. D. Levi and P. Winternitz, J. Phys. A 0305-4470 10.1088/0305-4470/22/15/ 010 22, 2915 (1989).
9. P. A. Clarkson and M. D. Kruskal, J. Math. Phys. 0022-2488 10.1063/1.528613 30, 2201 (1989).
10. S. -Y. Lou, Phys. Lett. A 0375-9601 10.1016/0375-9601(90)90178-Q 151, 133 (1990).
11. P. J. Olver, Proc. R. Soc. London, Ser. A 0950-1207 10.1098/rspa.1994. 0035 444, 509 (1994).
12. E. Pucci, J. Phys. A 0305-4470 10.1088/0305-4470/25/9/032 25, 2631 (1992).
13. D. J. Arrigo, P. Broadbridge, and J. M. Hill, J. Math. Phys. 0022-2488 10.1063/1.530365 34, 4692 (1993).
14. V. A. Baikov, R. K. Gazizov, and N. H. Ibragimov, Mat. Sb. 0368-8666 136, 435 (1988) V. A. Baikov, R. K. Gazizov, and N. H. Ibragimov, [Math. USSR. Sb. 64, 427 (1989)].
15. V. A. Baikov, R. K. Gazizov, and N. H. Ibragimov, in Approximate Transformation Groups and Deformations of Symmetry Lie Algebras, CRC Handbook of Lie Group Analysis of Differential Equations Vol. 3, edited by, N. H. Ibragimov, (CRC, Boca Raton, FL, 1996).
16. W. I. Fushchich and W. M. Shtelen, J. Phys. A 0305-4470 10.1088/0305-4470/22/18/007 22, L887 (1989).
17. M. Pakdemirli, M. Yurusoy, and I. T. Dolapci, Acta Appl. Math. 80, 243 (2004). 0167-8019
18. R. Wiltshire, J. Comput. Appl. Math. 0377-0427 10.1016/j.cam.2005.11.003 197, 287 (2006).
19. J. Boussinesq, Compt. Rend. 72, 755 (1871).
20. J. Boussinesq, J. Math. Pures Appl. 7, 55 (1872).
21. M. Toda, Phys. Rep.. 18, 1 (1975).
22. G. B. Whitham, Linear and Nonlinear Waves (Wiley, New York, 1974).
23. V. E. Zakharov, Sov. Phys. JETP 38, 108 (1974). 0038-5646
24. E. Infeld and G. Rowlands, Nonlinear Waves, Solitons and Chaos (Cambridge University Press, Cambridge, England, 1990).
25. P. Daripa, J. Comput. Appl. Math. 0377-0427 10.1016/S0377-0427(98)00186-1 100, 161 (1998).
26. P. Daripa and W. Hua, Appl. Math. Comput. 101, 159 (1999). 0096-3003
27. P. Daripa, Eur. J. Mech. B/Fluids 0997-7546 10.1016/j.euromechflu.2006. 02.003 25, 1008 (2006).
28. R. K. Dash and P. Daripa, Appl. Math. Comput. 0096-3003 10.1016/S0096-3003(01)00166-7 126, 1 (2002).