Wave interactions and the analysis of the perturbed Burgers equation

Physica D: Nonlinear Phenomena

Volumn 211, Issue 1-2, 2005, Pages 57-73

  Veksler, Alex ^a   Zarmi, Yair ^a  

^a BEN GURION UNIVERSITY OF THE NEGEV   (Israel)

Author keywords

Burgers equation; Normal Form expansion; Wave interactions

Indexed keywords

ASYMPTOTIC STABILITY; MATHEMATICAL MODELS; NUMERICAL ANALYSIS; WAVE EQUATIONS;

BURGERS EQUATIONS; NORMAL FORM EXPANSION; WAVE INTERACTION; WAVE SOLUTIONS;

PERTURBATION TECHNIQUES;

EID: 27144521624     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physd.2005.08.001     Document Type: Article

References (27)

1. J.M. Burgers The nonlinear Diffusion equation 1974 Reiedl Dordtrecht
2. V.I. Karpman Non-Linear Waves in Dispersive Media 1975 Pergamon Oxford
3. B.S. Kerner, S.L. Klenov, and P. Konhäuser Phys. Rev. E. 56 1997 4200
4. H. Poincaré New Methods of Celestial Mechanics 1993 American Institute of Physics
5. G.D. Birkhoff Dynamical Systems 1996 American Mathematical Society Providence
6. V.I. Arnold Geometrical Methods in the Theory of Ordinary Differential Equations 1988 Springer-Verlag New York
7. Y. Kodama, Normal form and solitons, in: M.J. Ablowitz et al. (Eds.), Topics in Soliton Theory and Exactly Solvable Nonlinear Equation, World Scientific, Singapore, 1987, pp. 319-340.
8. Y. Hiraoka, Y. Kodama, Normal Form and Solitons, Lecture notes, Euro Summer School 2001, The Isaac Newton Institute, Cambridge, 15-25 August 2002.
9. Y. Kodama, and T. Taniuti J. Phys. Soc. Jpn. 47 1979 1706
10. T. Fokas, and L. Luo Contemp. Math. 200 1996 85
11. R.A. Kraenkel, J.G. Pereira, and E.C. de Rey Neto Phys. Rev. E58 1998 2526
12. Y. Kodama, A.V. Mikhailov, Obstacles to asymptotic integrability, in: A.S. Fokas, I.M. Gelfand (Eds.), Algebraic Aspects of Integrable Systems, Birkhäuser, Boston, 1997, pp. 173-204.
13. P.D. Lax Comm. Pure Appl. Math. 21 1968 467
14. P.D. Lax Comm. Pure Appl. Math. 2 1975 141
15. A.R. Forsyth, Theory of Differential Equations. Part IV. Partial Differential Equations, Cambridge University Press, Cambridge, 1906 (republished by Dover, New York, 1959).
16. E. Hopf Comm. Pure Appl. Math. 3 1950 201 230
17. J.D. Cole Quart. Appl. Math. 9 1951 225 236
18. P.J. Olver Applications of Lie Groups to Differential Equations 1986 Springer-Verlag New York
19. S. Tao J. Phys. A: Math. Gen. 22 1989 3737
20. H. Tasso J. Phys. A 29 1996 7779
21. A.V. Samokhin Acta Appl. Math. 56 1999 253
22. G.B. Whitham Linear and Nonlinear Waves 1974 Wiley New York
23. J.W. Miles J. Fluid Mech. 79 1977 171
24. P.B. Kahn, and Y. Zarmi Nonlinear Dynamics: Exploration Through Normal Forms 1998 Wiley New York
25. L.A. Kalyakin Physica D 87 1995 193
26. A. Veksler, and Y. Zarmi WSEAS Trans. Math. 3 2004 560
27. A. Veksler, and Y. Zarmi Th. Math. Phys. 144 2005 1227 1237