Combined partial-bar and Riemann-Hilbert inverse methods for integrable non-linear evolution equations in (2+1) dimensions

Abstract

The authors give a natural combination of partial-bar and Riemann-Hilbert problem inverse methods for an n th-order scalar spectral problem which solves a number of integrable non-linear evolution equations in two space and one time (2+1) dimensions. The theory embraces the two Kadomtsev-Petviashvili equations (1970) and their lump solutions.