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

TL;DR

This paper proves a more general factorization formula for wave functions used in inverse spectral transforms, with applications and compatibility analysis for Bäcklund-Darboux transformations.

Contribution

It extends the factorization formula for wave functions in inverse spectral methods and explores related compatibility issues for Bäcklund-Darboux transformations.

Findings

Generalized the factorization formula for wave functions

Applied the formula to inverse spectral transform problems

Analyzed compatibility of Bäcklund-Darboux transformations

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 B\"acklund-Darboux transformation are treated too.