Traveling-wave solutions for Korteweg-de Vries-Burgers equations through factorizations. (English) Zbl 1110.35322
Summary: 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.
MSC:
| 35Q53 | KdV equations (Korteweg-de Vries equations) |
| 34L40 | Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) |
| 37K40 | Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems |
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