Asymptotics of coupled solutions of the Kadomtsev–Petviashvili equation

Abstract

We determine a subset in $\text{R}{}^2$ and a measure on this set which allow to construct coupled non-localized solutions of the KP-I equation, which are connected by the change of variables (x,t)↦(−x,−t), and split into asymptotic solitons as t→∞ in the neighbourhood of the leading edge of the solutions. The solitons corresponding to each of the solutions have different amplitudes and lines of constant phase.