A Criterion for the Solvability of the Cauchy Problem for Matrix Soliton Equations
Abstract
Abstract A criterion for the solvability of a holomorphic Cauchy problem for a certain class of matrix soliton equations is proved in terms of a scattering transform defined in a new way. For the equations under consideration, a method is indicated for constructing holomorphic solutions using the Zakharov-Shabat dressing method for the zero solution, as well as the possibility of extending the solutions with respect to the spatial variable to globally meromorphic functions.
Fields of Study & Subjects
Nonlinear Waves and Solitons
Mathematical functions and polynomials
Algebraic and Geometric Analysis
Publication details
- Journal / source
- Mathematical Notes
- Publisher
- Pleiades Publishing Ltd
- Volume
- 119
- Issue
- 1-2
- Pages
- 167–178
- Publication date
- 1 February 2026
- Language
- EN