Positon-like Solutions of Nonlinear Evolution Equations in (2+1) Dimensions

Positons are new exact solutions of classical nonlinear evolution equations in one spatial dimension, such as the Korteweg–de Vries and sine–Gordon equations. Recently, positons have been established as a singular limit of a 2-soliton expression. Extension to (2+1)-dimensional phenomena (2 spatial and 1 temporal dimensions) is attempted in this work, and positon-like solutions are obtained for the well-known Kadomtsev–Petviashvili and Davey–Stewartson equations, as well as less familiar examples such as the (2+1)-dimensional integrable sine–Gordon equation.