Multidimensional solitons and their spectral transforms

Abstract

The soliton solution to the hierarchy of two‐dimensional nonlinear evolution equations related to the Zakharov–Shabat spectral problem (including the Davey–Stewartson equation) are derived and studied. The solitons are localized two‐dimensional structures traveling on straight lines at constant velocities. Their spectral transform is not uniquely defined and this point is discussed by giving two explicit different spectral transforms of the one‐soliton solution and also by giving the general dependence of the spectral transform on the definition of the basic Jost‐like solutions.