Lie symmetry analysis and exact solutions for the short pulse equation

Nonlinear Analysis, Theory, Methods and Applications

Volumn 71, Issue 5-6, 2009, Pages 2126-2133

  Liu, Hanze ^a,b   Li, Jibin ^a,c  

^a KUNMING UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

^b BINZHOU UNIVERSITY   (China)

^c ZHEJIANG NORMAL UNIVERSITY   (China)

Author keywords

Generalized symmetry method; Lie symmetry analysis; Power series solution; Short pulse equation; Traveling wave solution

Indexed keywords

GENERALIZED SYMMETRY METHOD; LIE SYMMETRY ANALYSIS; POWER SERIES SOLUTION; SHORT PULSE EQUATION; TRAVELING WAVE SOLUTION;

MECHANICAL ENGINEERING;

EID: 67349250784     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2009.01.075     Document Type: Article

References (30)

1. Gardner C.S., Greene J.M., Kruskal M.D., and Miura R.M. Method for solving the Korteweg-de Vries equation. Phys. Rev. Lett. 19 (1967) 1095-1097
2. Li Y.S. Soliton and integrable systems. Advanced Series in Nonlinear Science (1999), Shanghai Scientific and Technological Education Publishing House, Shanghai (in Chinese)
3. Hirota R., and Satsuma J. A variety of nonlinear network equations generated from the Bäcklund transformation for the Tota lattice. Suppl. Prog. Theor. Phys. 59 (1976) 64-100
4. Liu H., et al. Exact periodic wave solutions for the hKdV equation. Nonlinear Anal. (2008) 10.1016/j.na.2008.03.019
5. Olver P.J. Applications of Lie Groups to Differential Equations. Grauate Texts in Mathematics vol. 107 (1993), Springer, New York
6. Bluman G.W., and Kumei S. Symmetries and Differential Equations (1989), Springer-Verlag World Publishing Gorp.
7. Cantwell B.J. Introduction to Symmetry Analysis (2002), Cambridge University Press
8. Liu H., et al. Lie symmetry analysis and exact explicit solutions for general Burgers' equation. J. Comput. Appl. Math. (2008) 10.1016/j.cam.2008.06.009
9. Clarkson P., and Kruskal M. New similarity reductions of the Boussinesq equation. J. Math. Phys. 30 10 (1989) 2201-2213
10. Clarkson P. New similarity reductions for the modified Boussinesq equation. J. Phys. A: Gen. 22 (1989) 2355-2367
11. Craddock M., and Platen E. Symmety group methods for fundamental solutions. J. Differential Equations 207 (2004) 285-302
12. Craddock M., and Lennox K. Lie group symmetries as integral transforms of fundamental solutions. J. Differential Equations 232 (2007) 652-674
13. Schäfer T., and Wayne C.E. Propagation of ultra-short optical pulses in cubic nonlinear media. Phys. D 196 (2004) 90-105
14. Sakovich A., and Sakovich S. J. Phys. A Math. Gen. 39 (2006) L361
15. Wadati M., Konno K., and Ichikawa Y. J. Phys. Soc. Japan 47 (1979) 1698
16. Brunelli J. J. Math. Phys. 46 (2005) 123507
17. Sakovich A., and Sakovich S. J. Phys. Soc. Japan 74 (2005) 239
18. Matsuno Y. J. Phys. Soc. Japan 76 (2007) 084003
19. Kuetche K., Bouetou B., and Kofane T. J. Phys. Soc. Japan 76 (2007) 024004
20. Parkes E. Chaos Solitons Fractals 38 (2008) 154
21. Li J. Sci. China Ser. A 50 (2007) 773
22. Li J., and Dai H. On the Study of Singular Nonlinear Traveling Wave Equations: Dynamical System Approach (2007), Science Press, Beijing
23. Zhang Y., and Li J. J. Phys. Soc. Japan 76 (2007) 116001
24. Tian C. Lie Groups and its Applications to Differential Equations (2001), Science Press, Beijing (in Chinese)
25. Liu H., and Qiu F. Analytic solutions of an iterative equation with first order derivative. Ann. Differential Equations 21 3 (2005) 337-342
26. Liu H., and Li W. Discussion on the analytic solutions of the second-order iterative differential equation. Bull. Korean Math. Soc. 43 4 (2006) 791-804
27. Liu H., and Li W. The exact analytic solutions of a nonlinear differential iterative equation. Nonlinear Anal. 69 (2008) 2466-2478
28. Asmar N.H. Partial Differential Equations with Fourier Series and Boundary Value Problems. second ed. (2005), China Machine Press, Beijing
29. Rudin W. Principles of Mathematical Analysis. third ed. (2004), China Machine Press, Beijing
30. Fichtenholz G.M. Functional Series (1970), Gordon & Breach, New York, London, Paris