Generalized matrix exponential solutions to the AKNS hierarchy
The authors consider the AKNS hierarchy and discuss its integrability in the framework of the modified inverse scattering transformation. The latter is essentially a consequence of the usual Gelfand-Levitan-Marchenko integral equation, and relies on a resulting pair of coupled Sylvester equations, which allow to write the explicit soliton solutions in matrix form. The key observation, that seems to simplify considerably the construction of the soliton solutions, is based on the freedom to choose a set of six matrices, subject to some week conditions, in order to produce the required pair of coupled Sylvester equations. This is clearly demonstrated by the authors by giving a number of explicit one- and multi-soliton solutions. The authors also generalize the AKNS hierarchy and their approach to integrability via a modified inverse scattering transformation. The paper is very straightforward, clearly written and is easy to follow. The authors also provide the complete details for their theorems and statements.
scientific article; zbMATH DE number 6991921
scientific article