Darboux transformation and exact solutions of nls-mb equations
Zhumageldina A.B. Yesmakhanova K.R. Pashen Zh.Zh.
2022al-Farabi Kazakh State National University
International Journal of Mathematics and Physics
2022#13Issue 236 - 43 pp.
A nonlinear wave is one of the basic objects of physics. They are inherent to plasma physics and solid state physics, gravity and nuclear physics, field theory and optics, hydrodynamics and aerodynamics, kinetics of chemical reactions and population dynamics. It is well known that the constuction of explicit solutions for an integrable system plays a significant part in the definition and explanation of nonlinear phenomena. In this article, we will focus on integrable nonlinear Schrodinger and Maxwell-Bloch equations (NLS-MB) that represents the propagation of optical impulses in an inhomogeneous fibreglass with erbiumdoped losses or amplification due to an external potential. Lax representation of NLS-MB will be given. Based on relevant Lax pair, Darboux transformation for NLS-MB will be obtained. Exact solutions will be derived through the Darboux transformation. Graphs of the obtained solutions will be constructed. By using our approach one can find also other differerent exact solutions of NLS-MB equations.
Darboux transformation , exact solutions , Lax pair , NLS-MB equations , soliton
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L.N. Gumilyov Eurasian National University, Astana, Kazakhstan
Ratbay Myrzakulov Eurasian International Centre for Theoretical Physics, Astana, Kazakhstan
L.N. Gumilyov Eurasian National University
Ratbay Myrzakulov Eurasian International Centre for Theoretical Physics
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