scholarly journals Darboux Transformation of the Second-Type Derivative Nonlinear Schrödinger Equation

2015 ◽  
Vol 105 (6) ◽  
pp. 853-891 ◽  
Author(s):  
Yongshuai Zhang ◽  
Lijuan Guo ◽  
Jingsong He ◽  
Zixiang Zhou
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Darboux Transformation ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
Derivative Nonlinear Schrödinger Equation

Darboux transformation of the second-type nonlocal derivative nonlinear Schrödinger equation

2019 ◽  
Vol 33 (10) ◽  
pp. 1950123 ◽  
Author(s):  
De-Xin Meng ◽  
Kuang-Zhong Li
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Darboux Transformation ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Darboux Transformations ◽  
First Order ◽  
Nonlinear Schrödinger ◽  
Derivative Nonlinear Schrödinger Equation

The second-type nonlocal derivative nonlinear Schrödinger (NDNLSII) equation is studied in this paper. By constructing its [Formula: see text]-order Darboux transformations (DT) from the first-order DT, Vandermonde-type determinant solutions of the NDNLSII equation are obtained from zero seed solutions, which would be singular unless the square of eigenvalues are purely imaginary.

DARBOUX TRANSFORMATION METHOD FOR GIVING SOLITON SOLUTIONS OF THE DERIVATIVE NONLINEAR SCHRÖDINGER EQUATION

1989 ◽  
Vol 04 (16) ◽  
pp. 1573-1579 ◽  
Author(s):  
ZONG-YUN CHEN ◽  
NIAN-NING HUANG
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Darboux Transformation ◽  
Schrodinger Equation ◽  
Soliton Solutions ◽  
Transformation Method ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
Derivative Nonlinear Schrödinger Equation ◽  
Jost Solutions

The so-called Darboux transformation method is presented for giving soliton solutions of the derivative nonlinear Schrödinger equation. With the help of the reduction transformation invariance, a possible form of the Darboux transformation is found simply. This method is more elementary and more simple as there is no need to discuss analyticities of the Jost solutions and time dependence of the scattering dates.

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