Exact solution in terms of elliptic functions for the Burgers-Korteweg-de Vries equation

Wave Motion

Volumn 38, Issue 2, 2003, Pages 109-115

  Feng, Zhaosheng ^a  

^a TEXAS A AND M UNIVERSITY   (United States)

Author keywords

Burgers KdV equation; Elliptic function; Exact solution; Solitary wave

Indexed keywords

DIFFERENTIAL EQUATIONS; MATHEMATICAL MODELS; NONLINEAR EQUATIONS;

ELLIPTIC FUNCTIONS;

MECHANICAL WAVES;

MATHEMATICAL METHOD;

EID: 0038079700     PISSN: 01652125     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0165-2125(03)00023-4     Document Type: Article

References (37)

1. Johnson R.S.A nonlinear equation incorporating damping and dispersion J. Fluid Mech. 42 1970 49-60
2. van Wijngaarden L.On the motion of gas bubbles in a perfect fluid Ann. Rev. Fluid Mech. 4 1972 369-373
3. Gao G.A theory of interaction between dissipation and dispersion of turbulence Sci. Sinica (Ser. A) 28 1985 616-627
4. Liu S.D. Liu S.K. KdV-Burgers equation modelling of turbulence Sci. Sinica (Ser. A) 35 1992 576-586
5. EGrua H. Hu P.W. Unified shock profile in a plasma Phys. Fluids 10 1967 2596-2602
6. G.B. Whitham, Linear and Nonlinear Waves, Springer, New York, 1974.
7. Toda M. Waves in nonlinear lattice Progr. Theor. Phys. Suppl. 45 1970 174-200
8. M.D. Kruskal, The Korteweg-de Vries Equation and Related Evolution Equations, American Mathematical Society, Providence, RI, 1974.
9. M.J. Ablowitz, H. Segur, Solitons and the Inverse Scattering Transform, SIAM, Philadelphia, 1981.
10. Love M.D.Subgrid modelling studies with Burgers equation J. Fluid Mech. 100 1980 87-110
11. Hirota R. Exact solution of the Korteweg-de Vries equation for multiple collisions of solitons Phys. Rev. Lett. 27 1971 1192-1194
12. Medina E. Hwa T. Kardar M. Zhang Y.C. Burgers' equation with correlated noise: renormalization-group analysis and applications to directed polymers and interface growth Phys. Rev. A 39 1989 3053-3075
13. Jeffrey A.Some aspects of the mathematical modelling of long nonlinear waves Arch. Mech. 31 1979 559-574
14. Canosa J. Gazdag J. The Korteweg-de Vries-Burgers equation J. Comput. Phys. 23 1977 393-403
15. K.Z. Dauletiyarov, Investigation of the difference method for the Bona-Smith and Burgers-Korteweg-de Vries equations, Zh. Vychisl. Mat. i Mat. Fiz. 24 (1984) 402 (Russian).
16. Turetaev I.D. Investigation of projection-difference schemes for the Bona-Smith and the Burgers-Korteweg-de Vries equations Comput. Math. Math. Phys. 31 1991 69-74
17. Bona J.L. Schonbek M.E. Traveling wave solutions to Korteweg-de Vries-Burgers equation Proc. R. Soc. Edin. A 101 1985 207-226
18. Guan K.Y. Gao G. The qualitative theory of the mixed Korteweg-de Vries-Burgers equation Sci. Sinica (Ser. A) 30 1987 64-73
19. Shu J.J.The proper analytical solution of the Korteweg-de Vries equation J. Phys. A (Math. Gen.) 20 1987 L49-L56
20. Gibbon J.D. Radmore P. Tabor M. Wood D. The Painleve and Hirota's method Stud. Appl. Math. 72 1985 39-63
21. Xiong S.L. An analytic solution of Burgers-KdV equation Chinese Sci. Bull. 34 1989 1158-1162
22. Liu S.D. Liu S.K. Ye Q.X. Explicit traveling wave solutions of nonlinear evolution equations Math. Pract. Theory 28 1998 289-301
23. Jeffrey A. Mohamad M.N.B. Exact solutions to the KdV-Burgers equation Wave Motion 14 1991 369-375
24. Jeffrey A. Xu S. Exact solutions to the Korteweg-de Vries-Burgers equation Wave Motion 11 1989 559-564
25. Halford W.D. Vlieg-Hulstman M. The Korteweg-de Vries-Burgers equation: a reconstruction of exact solutions Wave Motion 14 1991 267-271
26. Wang M. Exact solutions for a compound KdV-Burgers equation Phys. Lett. A 213 1996 279-287
27. Parkes E.J. Duffy B.R. Travelling solitary wave solutions to a compound KdV-Burgers equation Phys. Lett. A 229 1997 217-220
28. Feng Z. The first-integral method to the Burgers-Korteweg-de Vries equation J. Phys. A (Math. Gen.) 35 2002 343-349
29. Ablowitz M.J. Zeppetella A. Explicit solution of Fisher's equation for a special wave speed Bull. Math. Biol. 41 1979 835-840
30. Fan E. Zhang J. Hon B.Y. A new complex line soliton for the two-dimensional KdV-Burgers equation Phys. Lett. A 291 2001 376-380
31. Elwakil S.A. El-labany S.K. Zahran M.A. Sabry R. Modified extended tanh-function method for solving nonlinear partial differential equations Phys. Lett. A 299 2002 179-188
32. M. Abramowitz, I. Stegun, Handbook of Mathematical Functions, Dover, New York, 1965.
33. D.F. Lawden, Elliptic Functions and Applications, Springer, New York, 1989.
34. Li Z. Wang M. Travelling wave solutions to the two-dimensional KdV-Burgers equation J. Phys. A (Math. Gen.) 26 1993 6027-6031
35. Ma W. An exact solution to two-dimensional Korteweg-de Vries-Burgers equation J. Phys. A (Math. Gen.) 26 1993 L17-L20
36. Parkes E.J. Exact solutions to the two-dimensional Korteweg-de Vries-Burgers equation J. Phys. A (Math. Gen.) 27 1994 497-501
37. Feng Z. Fei S. Ji W. Exact solutions of a generalized Klein-Gordon equation Math. Pract. Theory 27 1997 220-226