Traveling-Wave Solutions for Korteweg–de Vries–Burgers Equations through Factorizations

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.