Traveling-wave solutions of the standard and compound form of Korteweg–de Vries–Burgers equations are found using factorizations of the corresponding reduced ordinary differential equations. The procedure leads to solutions of Bernoulli equations of non-linearity 3/2 and 2 (Riccati), respectively. Introducing the initial conditions through an imaginary phase in the traveling coordinate, we obtain all the solutions previously reported, some of them being corrected here, and showing, at the same time, the presence of interesting details of these solitary waves that have been overlooked before this investigation.
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References
Sahu B., and Roychoudhury R. (2003). Czech. J. Phys. 53:517
D. Zwillinger, Handbook of Differential Equations (Academic Press, 1992).
Canosa J. and Gazdag J. (1977). J. Comput. Phys. 23:393
Parkes E.J., and Duffy B.R. (1997). Phys. Lett. A 229:217
Parkes E.J. (2003). Phys. Lett. A 317:424
Wang M. (1996). Phys. Lett. A 213:279
Tie-Cheng X., Hong-Qing Z., Zhen-Ya Y. (2001). Chin. Phys. 10:694
Antar N., Int. J. Eng. Sci. 40, 1179 (2002); I. Bakirtaş and Antar N., Int. J. Eng. Sci. 41, 1163 (2003).
Shukla P.K., and Tagare S.G. (1976). Phys. Lett. A 59:38
Nakamura Y., Bailung H., and Shukla P.K. (1999). Phys. Rev. Lett. 83:1602
Kawahara T., Toh S. (1985). Phys. Fluids 28:1636
Webb G.M., and Zank G.P., Astophys. J. 396, 549 (1992); Zank G.P., Astrophys. Sp. Sci. 140, 301 (1988).
Muskens O.L., and Dijkhuis J.I., Phys. Rev. Lett. 89, 285504 (2002).
Kivshar Y.S. (1990). Phys. Rev. A 42:1757
E. Schrödinger, Proc. Roy. Irish. Acad. A 46, 9 (1940); Proc. Roy. Irish. Acad. A 47, 53 (1941).
Infeld L. and Hull T.E. (1951). Rev. Mod. Phys. 23:21
B. Mielnik and O. Rosas-Ortiz, J. Phys. A 37, 10007 (2004).
Berkovich L.M. (1992). Sov. Math. Dokl. 45:162
Rosu H.C., and O. Cornejo-Pérez, Phys. Rev. E 71, 046607 (2005).
Feng Z. (2002). Phys. Lett. A 293:57
Feng Z. (2003). Phys. Lett. A 312:65
Feng Z. and Chen G. (2005). Physica A 352:419
Liu C., Liu X. (2004). Phys. Lett. A 331:393
Demiray H. (2005). Appl. Math. Comp. 162:925
Xue J.-K. (2003). Eur. Phys. J. D 26:211
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Cornejo-Pérez, O., Negro, J., Nieto, L.M. et al. Traveling-Wave Solutions for Korteweg–de Vries–Burgers Equations through Factorizations. Found Phys 36, 1587–1599 (2006). https://doi.org/10.1007/s10701-006-9069-5
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DOI: https://doi.org/10.1007/s10701-006-9069-5