Symmetries and solutions of the three-dimensional Kadomtsev — Petviashvili equation

Abstract: A symmetry group of the three-dimensional Kadomtsev — Petviashvili equation is calculated. An example of an invariant solution is given. Exact solutions for the equation under study in the form of double waves are revealed. The resulting solutions are expressed in terms of elementary functions and describe an interaction between a pair of solitons. Smooth bounded rational solutions are also constructed.

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

Audience: researchers in the topic

Mathematical models and integration methods