Darboux transformations and global solutions for a nonlocal derivative nonlinear Schrodinger equation

TL;DR

This paper introduces a nonlocal derivative nonlinear Schrödinger equation, constructs Darboux transformations to generate explicit solutions, and identifies conditions for obtaining global bounded solutions.

Contribution

It develops Darboux transformation techniques for a nonlocal derivative NLS equation and derives conditions for global solutions, advancing solution methods for nonlocal integrable systems.

Findings

Explicit Darboux transformations of degrees one and two constructed.

Global bounded solutions obtained through specific eigenvalue and parameter choices.

Solutions derived from zero seed solution exhibit controlled singularities.

Abstract

A nonlocal derivative nonlinear Schrodinger equation is introduced. By constructing its basic Darboux transformations of degrees one and two, the explicit expressions of new solutions are derived from seed solutions by Darboux transformation of degree 2n. Usually the derived solutions of this nonlocal equation may have singularities. However, by suitable choice of eigenvalues and the parameters describing the ratio of the two entries of the solutions of the Lax pair, global bounded solutions of the nonlocal derivative nonlinear Schrodinger equation are obtained from zero seed solution by a Darboux transformation of degree 2n.