Solitary waves in the cylindrical Kadomtsev–Petviashvili equation

Abstract: We present exact solutions in the form of solitary waves in the cylindrical Kadomtsev–Petviashvili (cKP) equation (alias Johnson equation) which describes nonlinear wave processes in dispersive media. This equation belongs to the class of completely integrable systems; however, its exact solutions were not studied in detail albeit some particular solutions were found. We show that this equation has relationships with the classical Korteweg–de Vries and plane Kadomtsev–Petviashvili equations. Using these relationships, some new solutions can be formally obtained that represent cylindrically diverging solitary waves and compact solitary waves called lumps. We demonstrate interesting properties of lumps solutions specific for the cylindrical geometry. Exact solutions describing normal and anomalous lump interactions are found and graphically illustrated.

mathematical physicsanalysis of PDEsclassical analysis and ODEsdynamical systemsnumerical analysisexactly solvable and integrable systemsfluid dynamics

Audience: researchers in the topic

Mathematical models and integration methods