Local and global well-posedness of the Maxwell-Bloch system of equations with inhomogeneous broadening
DOI10.1515/anona-2024-0054MaRDI QIDQ6655653
G. Biondini, Zechuan Zhang, B. Prinari
Publication date: 27 December 2024
Published in: Advances in Nonlinear Analysis (Search for Journal in Brave)
inverse scattering transformwell-posednessintegrable systemsMaxwell-Bloch equationsinhomogeneous broadening
PDEs in connection with optics and electromagnetic theory (35Q60) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) NLS equations (nonlinear Schrödinger equations) (35Q55) Lasers, masers, optical bistability, nonlinear optics (78A60) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)
Cites Work
- Title not available (Why is that?)
- Title not available (Why is that?)
- Title not available (Why is that?)
- Title not available (Why is that?)
- Title not available (Why is that?)
- Title not available (Why is that?)
- Global well-posedness on the derivative nonlinear Schrödinger equation
- Global well-posedness for the derivative nonlinear Schrödinger equation in \(H^{\frac {1}{2}} (\mathbb{R})\)
- Complete asymptotic representation of an electromagnetic pulse in a long two-level amplifier
- The initial-boundary-value problem for the 1D nonlinear Schrödinger equation on the half-line.
- On a class of nonlinear Schrödinger equations. II. Scattering theory, general case
- Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. I: Schrödinger equations
- Nonelliptic Schrödinger equations
- Polarization switching of light interacting with a degenerate two-level optical medium
- Nonhomogeneous boundary-value problems for one-dimensional nonlinear Schrödinger equations
- On nonlinear Schrödinger equations. II: \(H^ S\)-solutions and unconditional well-posedness
- Global well-posedness for the derivative nonlinear Schrödinger equation
- Global well-posedness for the nonlinear Schrödinger equation with derivative in energy space
- The nonlinear Schrödinger equation on the half-line
- Inverse scattering transform for 3-level coupled Maxwell-Bloch equations with inhomogeneous broadening
- Direct and inverse scattering transforms with arbitrary spectral singularities
- The cauchy problem for the critical nonlinear Schrödinger equation in Hs
- Coupling constant behavior of eigenvalues of Zakharov-Shabat systems
- Scattering and inverse scattering for first order systems
- L2-Sobolev space bijectivity of the scattering and inverse scattering transforms
- Long‐time asymptotics for solutions of the NLS equation with initial data in a weighted Sobolev space
- On the Eigenvalues of Zakharov--Shabat Systems
- Existence of Global Solutions to the Derivative NLS Equation with the Inverse Scattering Transform Method
- Stopping a slow-light soliton: an exact solution
- Driving slow-light solitons by a controlling laser field
- A Refined Global Well-Posedness Result for Schrödinger Equations with Derivative
- Sharp global well-posedness for KdV and modified KdV on ℝ and 𝕋
- Microlocal dispersive smoothing for the Schrödinger equation
- Inverse scattering transform for the focusing nonlinear Schrödinger equation with counterpropagating flows
- Inverse scattering transform for two-level systems with nonzero background
- A Robust Inverse Scattering Transform for the Focusing Nonlinear Schrödinger Equation
- Coherence in Spontaneous Radiation Processes
- Introduction to nonlinear dispersive equations
- On the Maxwell‐Bloch system in the sharp‐line limit without solitons
- On Maxwell-Bloch systems with inhomogeneous broadening and one-sided nonzero background
This page was built for publication: Local and global well-posedness of the Maxwell-Bloch system of equations with inhomogeneous broadening
Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6655653)
