Determinant representation of Darboux transformation for the (2+1)-dimensional nonlocal nonlinear Schrödinger-Maxwell-Bloch equations

Optik ◽  
2021 ◽  
Vol 228 ◽  
pp. 166150
Author(s):  
Jiang-Yan Song ◽  
Chi-Ping Zhang ◽  
Yu Xiao
Keyword(s):  
Darboux Transformation ◽  
Bloch Equations ◽  
Nonlinear Schrödinger ◽  
Determinant Representation ◽  
Nonlocal Nonlinear ◽  
Maxwell Bloch Equations

Determinant Representation of Binary Darboux Transformation for the AKNS Equation

2015 ◽  
Vol 70 (12) ◽  
pp. 1039-1048 ◽  
Author(s):  
Jing Yu ◽  
Jingwei Han ◽  
Jingsong He
Keyword(s):  
Darboux Transformation ◽  
Darboux Transformations ◽  
Nls Equation ◽  
Reduction Condition ◽  
Nonlinear Schrödinger ◽  
Determinant Representation ◽  
Akns Equation ◽  
New Form ◽  
Binary Darboux Transformation

AbstractIn this paper, the determinant representation of the n-fold binary Darboux transformation, which is a 2×2 matrix, for the Ablowitz–Kaup–Newell–Segur equation is constructed. In this 2×2 matrix, each element is expressed by (2n+1)-order determinants. When the reduction condition r=–q̅ is considered, we obtain one of binary Darboux transformations for the nonlinear Schrödinger (NLS) equation. As its applications, several solutions are constructed for the NLS equation. Especially, a new form of two-soliton is given explicitly.

DETERMINANT REPRESENTATION OF N-TIMES DARBOUX TRANSFORMATION FOR THE DEFOCUSING NONLINEAR SCHRÖDINGER EQUATION

2013 ◽  
Vol 27 (29) ◽  
pp. 1350216 ◽  
Author(s):  
JINGWEI HAN ◽  
JING YU ◽  
JINGSONG HE
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Soliton Solution ◽  
Darboux Transformation ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Nls Equation ◽  
Nonlinear Schrödinger ◽  
Determinant Representation

The determinant expression T[N] of a new Darboux transformation (DT) for the Ablowitz–Kaup–Newell–Segur equation are given in this paper. By making use of this DT under the reduction r = q*, we construct determinant expressions of dark N-soliton solution for the defocusing NLS equation. Except known one-soliton, we provide smooth two-soliton and smooth N-soliton on a certain domain of parameter for the defocusing NLS equation.

scholarly journals Single and Multi-Soliton Solutions for a Spectrally Deformed Set of Maxwell-Bloch Equations

Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 435
Author(s):  
Mehmet Baran
Keyword(s):  
Nonlinear Optics ◽  
Darboux Transformation ◽  
Soliton Solutions ◽  
Bloch Equations ◽  
Spectral Deformation ◽  
Maxwell Bloch Equations

A specific spectral deformation of the Maxwell-Bloch equations of nonlinear optics is investigated. The Darboux transformation formalism is adapted to this spectrally deformed system to construct its single and multi-soliton solutions. The Effects of spectral deformation on soliton behaviour is studied.

Solitons for the (2+1)-dimensional nonlinear Schrödinger-Maxwell-Bloch equations in an erbium-doped fibre

2015 ◽  
Vol 63 (6) ◽  
pp. 590-597 ◽  
Author(s):  
Xiao-Yu Wu ◽  
Bo Tian ◽  
Hui-Ling Zhen ◽  
Wen-Rong Sun ◽  
Ya Sun
Keyword(s):  
Bloch Equations ◽  
Nonlinear Schrödinger ◽  
Erbium Doped ◽  
Maxwell Bloch Equations

Darboux transformation and the exact solutions of the (2+1)-dimensional nonlocal complex modified Korteweg-de Vries and Maxwell–Bloch equations

2020 ◽  
Vol 34 (22) ◽  
pp. 2050230
Author(s):  
Na-Na Li ◽  
Hui-Qin Hao ◽  
Rui Guo
Keyword(s):  
Exact Solutions ◽  
Darboux Transformation ◽  
Soliton Solutions ◽  
Lax Pair ◽  
Darboux Transformations ◽  
Bloch Equations ◽  
Dynamic Behaviors ◽  
De Vries ◽  
Maxwell Bloch Equations

In this paper, we consider the (2[Formula: see text]+[Formula: see text]1)-dimensional nonlocal complex modified Korteweg-de Vries and Maxwell–Bloch (cmKdV-MB) equations. According to the relevant Lax pair presented, we construct one- and two-fold Darboux transformations (DT). The exact solutions are derived from the trivial seeds by DT and the dynamic behaviors of soliton solutions are analyzed by individual pictures.

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