Darboux transformation and exact solutions of NLS-MB equations

A.B. Zhumageldina; K.R. Yesmakhanova; Zh.Zh. Pashen

doi:10.26577/ijmph.2022.v13.i2.05

Darboux transformation and exact solutions of NLS-MB equations

Authors

A.B. Zhumageldina L.N. Gumilyov Eurasian National University, Astana, Kazakhstan http://orcid.org/0000-0002-5795-226X
K.R. Yesmakhanova L.N. Gumilyov Eurasian National University, Astana, Kazakhstan http://orcid.org/0000-0002-4305-5939
Zh.Zh. Pashen L.N. Gumilyov Eurasian National University, Astana, Kazakhstan http://orcid.org/0000-0002-3751-3278

DOI:

https://doi.org/10.26577/ijmph.2022.v13.i2.05

126 121

Abstract

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 construction 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 fiberglass with erbium-doped 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.

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How to Cite

Zhumageldina, A., Yesmakhanova, K., & Pashen, Z. (2023). Darboux transformation and exact solutions of NLS-MB equations. International Journal of Mathematics and Physics, 13(2), 36–43. https://doi.org/10.26577/ijmph.2022.v13.i2.05

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Issue

Vol. 13 No. 2 (2022): International Journal of Mathematics and Physics

Section

PHYSICS

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