High Order Solutions and Generalized Darboux Transformations of Derivative Schr\"odinger Equation
Boling Guo, Liming Ling, Q. P. Liu
TL;DR
This paper develops generalized Darboux transformations for the derivative nonlinear Schrödinger equation, enabling the derivation of high order solutions expressed via determinants, advancing solution techniques for DNLS.
Contribution
The paper introduces two new types of generalized Darboux transformations for DNLS, providing explicit solution formulas and enabling the calculation of high order solutions.
Findings
Derived two solution formulas for DNLS using determinants.
Constructed high order solutions for DNLS.
Established generalized Darboux transformations via limit techniques.
Abstract
By means of certain limit technique, two kinds of generalized Darboux transformations are constructed for the derivative nonlinear Sch\"odinger equation (DNLS). These transformations are shown to lead to two solution formulas for DNLS in terms of determinants. As applications, several different types of high order solutions are calculated for this equation.
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