Zakharov–Shabat system and hyperbolic pseudoanalytic function theory

摘要

In J. Phys. A: Math. Theor. 2008; 41:65205 a hyperbolic analogue of pseudoanalytic function theory was developed. In the present contribution we show that one of the central objects of the inverse problem method, the Zakharov–Shabat system is closely related to a hyperbolic Vekua equation for which among other results a generating sequence and hence a complete system of formal powers can be constructed explicitly.