Travelling wave solutions of two-dimensional Korteweg–de Vries–Burgers and Kadomtsev–Petviashvili equations

The travelling wave solutions of the two-dimensional Korteweg–de Vries–Burgers and Kadomtsev–Petviashvili equations are studied from two complementary points of view. The first one is an adaptation of the factorization technique that provides particular as well as general solutions. The second one applies the Painlevé analysis to both equations, throwing light on some aspects of the first method and giving an explanation to some restriction on the coefficients, as well as the relation between factorizations and integrals of motion.