scholarly journals Darboux transformations and solutions of nonlocal Hirota and Maxwell–Bloch equations

2021 ◽  
Author(s):  
Ling An ◽  
Chuanzhong Li ◽  
Lixiang Zhang
Keyword(s):  
Darboux Transformations ◽  
Bloch Equations ◽  
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.

Numerical solutions to 2D Maxwell–Bloch equations

2008 ◽  
Vol 40 (5-6) ◽  
pp. 447-453 ◽  
Author(s):  
Jingyi Xiong ◽  
Max Colice ◽  
Friso Schlottau ◽  
Kelvin Wagner ◽  
Bengt Fornberg
Keyword(s):  
Numerical Solutions ◽  
Bloch Equations ◽  
Maxwell Bloch Equations

TIME AVERAGING OF IRREGULAR SPATIOTEMPORAL PATTERNS OF A LARGE APERTURE LASER IN TRANSITORY REGIME

2001 ◽  
Vol 11 (06) ◽  
pp. 1771-1779
Author(s):  
F. ENCINAS-SANZ ◽  
I. LEYVA ◽  
J. M. GUERRA
Keyword(s):  
Experimental Technique ◽  
Exposure Time ◽  
Time Integration ◽  
Spatiotemporal Patterns ◽  
Time Averaging ◽  
Bloch Equations ◽  
Ordered Structures ◽  
Large Aperture ◽  
Spatiotemporal Behavior ◽  
Maxwell Bloch Equations

By means of a new experimental technique, we measure quasi-intantaneous transverse intensity patterns in the gain-switch peak of a transversely excited atmospheric CO 2 laser with large aperture. The patterns recorded with a 2 ns resolution show a completely irregular spatiotemporal behavior, but when the exposure time of the measurements increases, boundary-determined ordered structures can be observed. As a quantification of this averaging process, the contrast of the intensity distributions decreases as the time integration grows. The results are numerically reproduced by integration of the full Maxwell–Bloch equations.

LIE–TROTTER FORMULA AND POISSON DYNAMICS

1999 ◽  
Vol 09 (03) ◽  
pp. 555-559 ◽  
Author(s):  
MIRCEA PUTA
Keyword(s):  
Rigid Body ◽  
Euler Equations ◽  
Bloch Equations ◽  
Free Rigid Body ◽  
Trotter Formula ◽  
Maxwell Bloch Equations

We construct via the Lie–Trotter formula some explicit Poisson integrators for the Maxwell–Bloch equations from laser-matter dynamics, the Euler equations of the free rigid body and the equations of the rigid body with a spinning rotor.

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