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.

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.

Darboux transformation and new soliton solutions for the (2+1)-dimensional complex modified Korteweg–de Vries and Maxwell–Bloch equations

2018 ◽  
Vol 32 (23) ◽  
pp. 1850277 ◽  
Author(s):  
Rui Guo ◽  
Run Zhou ◽  
Xiao-Mei Zhang ◽  
Yu-Zhen Chai
Keyword(s):  
Symbolic Computation ◽  
Darboux Transformation ◽  
Soliton Solutions ◽  
Lax Pair ◽  
Dynamic Features ◽  
Bloch Equations ◽  
De Vries ◽  
Maxwell Bloch Equations

In this paper, we focus on the (2[Formula: see text]+[Formula: see text]1)-dimensional complex modified Korteweg–de Vries and Maxwell–Bloch (CMKdV-MB) equations. According to the relevant Lax pair, the n-fold Darboux transformation (DT) is constructed. In addition, via the DT and symbolic computation, two different kinds of soliton solutions are derived from trivial seed solutions. Meanwhile, the dynamic features of soliton solutions are graphically analyzed.

N-soliton solutions for the Maxwell–Bloch equations via the Riemann–Hilbert approach

2021 ◽  
pp. 2150356
Author(s):  
Yan Li ◽  
Jian Li ◽  
Ruiqi Wang
Keyword(s):  
Spectral Analysis ◽  
Exact Solutions ◽  
Soliton Solutions ◽  
Lax Pair ◽  
Bloch Equations ◽  
Jump Matrix ◽  
Maxwell Bloch Equations

We mainly study [Formula: see text]-soliton solutions for the Maxwell–Bloch equations via the Riemann–Hilbert (RH) approach in this paper. The relevant RH problem has been constructed by performing spectral analysis of Lax pair. Then the jump matrix of the Maxwell–Bloch equations has been obtained. Finally, we gain the exact solutions of the Maxwell–Bloch equations by solving the special RH problem with reflectionless case.

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