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arXiv · 0909.1537

On the GBDT version of the B\"acklund-Darboux transformation and its applications to the linear and nonlinear equations and Weyl theory

Alexander Sakhnovich
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Abstract

A general theorem on the GBDT version of the B\"acklund-Darboux transformation for systems rationally depending on the spectral parameter is treated and its applications to nonlinear equations are given. Explicit solutions of direct and inverse problems for Dirac-type systems, including systems with singularities, and for the system auxiliary to the $N$-wave equation are reviewed. New results on explicit construction of the wave functions for radial Dirac equation are obtained.

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Alexander Sakhnovich. 2009-09-08. On the GBDT version of the B\"acklund-Darboux transformation and its applications to the linear and nonlinear equations and Weyl theory. https://arxiv.org/abs/0909.1537

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