Department of Mathematics
Recep Tayyip Erdogan University
53100 Rize, Turkey
email: mehmet.unlu@erdogan.edu.tr
Mehmet Unlu
Abstract:
We present a method for solving the integrable systems of nonlinear partial differential
equations, known as the derivative nonlinear Schrodinger II system (DNSL II system),
also called the Chen-Lee-Liu system.
This is done by presenting a solution technique for the inverse scattering problem
for the corresponding linear system of ordinary differential equations with
energy-dependent potentials.
The relevant inverse scattering problem is solved by establishing a system of linear
integral equations, which we refer to as the Marchenko system of linear integral equations.
In solving the inverse scattering problem we use the input data set consisting of a
transmission coefficient, a reflection coefficient, and the bound-state information
presented in the form of a pair of matrix triplets.
Using our data set as input to the Marchenko system, we recover the
potentials from the solution to the Marchenko system.
By using the time-evolved input data set, we recover the time-evolved
potentials, where those potentials form a solution to the integrable DNLS II system.
Submitted July 23, 2025. Published October 14, 2025.
Math Subject Classifications: 35Q55, 37K10, 37K15, 37K30, 34A55, 34L25, 34L40, 47A40.
Key Words: Inverse scattering; first-order linear system; Marchenko method;
derivative nonlinear Schrodinger equations; Chen-Lee-Liu system.
DOI: 10.58997/ejde.2025.97
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Mehmet Unlu Department of Mathematics Recep Tayyip Erdogan University 53100 Rize, Turkey email: mehmet.unlu@erdogan.edu.tr |
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