Zakharov-Shabat system and hyperbolic pseudoanalytic function theory. (English) Zbl 1196.30043
Pseudoanalytic function theory represents a far-reaching generalization of analytic function theory and corresponds to a generalized Cauchy-Riemann system, known as the Vekua equation. Recently, a hyperbolic analogue of pseudoanalytic function theory was developed. In the paper under review, the authors show that one of the central objects of the inverse problem method, the Zakharov-Shabat system, is closely related to a hyperbolic Vekua equation. Moreover, the authors are able to construct explicitly the corresponding generating sequence.
Reviewer: George Csordas (Honolulu)
MSC:
| 30G20 | Generalizations of Bers and Vekua type (pseudoanalytic, \(p\)-analytic, etc.) |
| 37K15 | Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems |
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