Abstract:
The inverse scattering method is used to construct general solutions of the Maxwell–Bloch system, these solutions being determined by specification of the polarization as $t\to\infty$. The solutions are classified. An approximate solution is obtained for the mixed boundary-value problem for the Maxwell–Bloch system describing the phenomenon of superfluorescence (generation of a pulse from initial fluctuations of the polarization in a mirrorless laser).
Citation:
I. R. Gabitov, V. E. Zakharov, A. V. Mikhailov, “Maxwell–Bloch equation and the inverse scattering method”, TMF, 63:1 (1985), 11–31; Theoret. and Math. Phys., 63:1 (1985), 328–343
This publication is cited in the following 72 articles:
Chen-Di Zhu, Jing Kang, Long-Xing Li, “Conservation Laws, Darboux Transformation and Soliton Solutions of a Negative Order Generalized Ablowitz-Kaup-Newell-Segur System”, Int J Theor Phys, 64:3 (2025)
Sitai Li, “On Zero-Background Solitons of the Sharp-Line Maxwell–Bloch Equations”, Commun. Math. Phys., 406:4 (2025)
Sitai Li, Peter D. Miller, “On the Maxwell‐Bloch system in the sharp‐line limit without solitons”, Comm Pure Appl Math, 77:1 (2024), 457
Asela Abeya, Gino Biondini, Gregor Kovačič, Barbara Prinari, “On Maxwell-Bloch Systems with Inhomogeneous Broadening and One-sided Nonzero Background”, Commun. Math. Phys., 405:8 (2024)
Gino Biondini, Barbara Prinari, Zechuan Zhang, “Local and global well-posedness of the Maxwell-Bloch system of equations with inhomogeneous broadening”, Advances in Nonlinear Analysis, 13:1 (2024)
M. Filipkovska, “Initial-Boundary Value Problem for the Maxwell–Bloch Equations with an Arbitrary Inhomogeneous Broadening and Periodic Boundary Function”, SIGMA, 19 (2023), 096, 39 pp.
Xin Wang, Jingsong He, “Darboux transformation and general soliton solutions for the reverse space–time nonlocal short pulse equation”, Physica D: Nonlinear Phenomena, 446 (2023), 133639
Volodymyr Kotlyarov, Oleksandr Minakov, “Maxwell–Bloch equations without spectral broadening: the long-time asymptotics of an input pulse in a long two-level laser amplifier”, Nonlinearity, 36:9 (2023), 5007
Mansur I. Ismailov, Cihan Sabaz, “Inverse Scattering Method via Riemann–Hilbert Problem for Nonlinear Klein–Gordon Equation Coupled with a Scalar Field”, J. Phys. Soc. Jpn., 92:10 (2023)
Xin Wang, Lei Wang, Chong Liu, Bowen Guo, Jiao Wei, “Rogue waves, semirational rogue waves and W-shaped solitons in the three-level coupled Maxwell–Bloch equations”, Communications in Nonlinear Science and Numerical Simulation, 107 (2022), 106172
Jin-Yan Zhu, Yong Chen, “Long-time asymptotic behavior of the coupled dispersive AB system in low regularity spaces”, Journal of Mathematical Physics, 63:11 (2022)
Xin Wang, Lei Wang, Jiao Wei, Bowen Guo, Jingfeng Kang, “Rogue waves in the three-level defocusing coupled Maxwell–Bloch equations”, Proc. R. Soc. A., 477:2256 (2021)
M. S. Filipkovska, V. P. Kotlyarov, “Propagation of electric field generated by periodic pumping in a stable medium of two-level atoms of the Maxwell–Bloch model”, Journal of Mathematical Physics, 61:12 (2020)
Gino Biondini, Ildar Gabitov, Gregor Kovačič, Sitai Li, “Inverse scattering transform for two-level systems with nonzero background”, Journal of Mathematical Physics, 60:7 (2019)
Vladimir P. Kotlyarov, “A Matrix Baker–Akhiezer Function Associated with the Maxwell–Bloch Equations and their Finite-Gap Solutions”, SIGMA, 14 (2018), 082, 27 pp.
Sitai Li, Gino Biondini, Gregor Kovačič, Ildar Gabitov, “Resonant optical pulses on a continuous-wave background in two-level active media”, EPL, 121:2 (2018), 20001
Vl. V. Kocharovsky, V. V. Zheleznyakov, E. R. Kocharovskaya, V. V. Kocharovsky, “Superradiance: the principles of generation and implementation in lasers”, Phys. Usp., 60:4 (2017), 345–384
M. S. Filipkovska, V. P. Kotlyarov, E. A. Melamedova (Moskovchenko), “Maxwell–Bloch equations without spectral broadening: gauge equivalence, transformation operators and matrix Riemann–Hilbert problems”, Zhurn. matem. fiz., anal., geom., 13:2 (2017), 119–153
Lihua Zhang, Fengsheng Xu, Lixin Ma, “Optimal system, group invariant solutions and conservation laws of the CGKP equation”, Nonlinear Dyn, 88:4 (2017), 2503