On the factorization formula for fundamental solutions in the inverse spectral transform

Abstract

A factorization formula for wave functions, which is basic in the inverse spectral transform approach to initial-boundary value problems, is proved in greater generality than before. Applications follow. Related compatibility questions for the GBDT version of Bäcklund-Darboux transformation are treated too.

Skew-Self-Adjoint Dirac System with a Rectangular Matrix Potential: Weyl Theory, Direct and Inverse Problems

“…The compatibility condition was studied in a more rigorous way and the corresponding important factorization formula for fundamental solutions was introduced in [38,40]. It was proved in greater detail and under weaker conditions in [34]. More specifically, we have the following proposition.…”

“…Proposition 4.2 [34]. Let m × m matrix functions G and F and their derivatives G t and F x exist on the semi-strip…”

KdV Equation in the Quarter–Plane: Evolution of the Weyl Functions and Unbounded Solutions

“…This evolution is an important component of the solution of the initial-boundary value problem. For simplicity, we derive the evolution under condition that F and G are continuously differentiable, though the requirement of the continuous differentiability could be weakened using the results from [13].…”