Solitary waves of the Korteweg-de Vries-Burgers' equation

Computer Physics Communications

Volumn 126, Issue 3, 2000, Pages 207-218

  Zaki, S I ^a  

^a SUEZ CANAL UNIVERSITY   (Egypt)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; CONVERGENCE OF NUMERICAL METHODS; ERROR ANALYSIS; FINITE ELEMENT METHOD; GALERKIN METHODS; MATHEMATICAL MODELS; NONLINEAR EQUATIONS;

BUBNOV-GALERKIN METHOD; KORTEWEG-DE VRIES-BURGER'S (KDVB) EQUATION;

PARTIAL DIFFERENTIAL EQUATIONS;

EID: 0034635943     PISSN: 00104655     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0010-4655(99)00470-1     Document Type: Article

References (18)

1. xx, Comm. Pure Appl. Math. 9 (1950) 210.
2. J.D. Cole, On a quasilinear parabolic equation occurring in aerodynamics, Quart. Appl. Math. 9 (1951) 225.
3. J. Burgers, A mathematical model illustrating the theory of turbulence, in: Adv. in Appl. Math. (Academic Press, NY, 1948).
4. N.J. Zabusky, A synergetic approach to problem of non-linear dispersive wave propagation and interaction, in: Proc. Symp. Non-linear PDES (Academic Press, NY, 1967).
5. B. Fornberg, G.B. Whitham, A numerical study of certain non-linear wave phenomena, Phil. Trans. Roy. Soc. 289 (1978) 373.
6. C.H. Su, C.S. Gardner, Derivation of the Korteweg-de Vries and Burgers' equation, J. Math. Phys. 10 (1969) 536.
7. H. Grad, P.N. Hu, Unified shock profile in a plasma, Phys. Fluids 10 (1967) 2596.
8. R.S. Johnson, A non-linear equation incorporating damping and dispersion, J. Fluid Mech. 42 (1970) 49.
9. R.S. Johnson, Shallow water waves in a viscous fluid, the undular bore, Phys. Fluids 15 (1972) 1693.
10. J. Canosa, J. Gazdag, The Korteweg-de Vries-Burgers' equation, J. Comp. Phys. 23 (1977) 393.
11. A.H.A. Ali, L.R.T. Gardner, G.A. Gardner, Numerical study of the KdVB equation using B-spline finite elements, J. Math. Phys. Sci. 27 (1) (1993) 37.
12. L.R.T. Gardner, G.A Gardner, A.H.A. Ali, Simulations of solitons using quadratic spline finite elements, Comput. Methods Appl. Mech. Engrg. 92 (1991) 231.
13. L.R.T. Gardner, G.A. Gardner, T. Geyikli, Comput. Methods Appl. Mech. Engrg. 124 (1995) 321.
14. A.H.A. Ali, G.A. Gardner, L.R.T. Gardner, A collocation solution for Burgers' equation using cubic B-spline finite elements, Comput. Methods Appl. Mech. Engrg. 100 (1992) 325.
15. A. Jeffrey, T. Kakutani, Weak non-linear dispersive waves: A discussion centered around the KdV equation, SIAM Rev. 14 (1972) 522.
16. V.I. Karpman, An asymptotic solution to the KdV equation, Soviet Phys. JEPT 25 A (1967) 708.
17. Yu.A. Berezin, V.I. Karpman, Non-linear evolution of disturbances in plasmas and other dispersive media, Soviet Phys. JETP 24 (1967) 1049.
18. K. Goda, On stability of some finite difference schemes for the KdV equation, J. Phys. Soc. Japan 39 (1975) 229.