Wave operators for the matrix Zakharov–Shabat system

DOI10.1063/1.3377048zbMath1310.81056OpenAlexW1998222582MaRDI QIDQ5249538

Martin Klaus, Cornelis V. M. van der Mee

Publication date: 6 May 2015

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.3377048

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) (S)-matrix theory, etc. in quantum theory (81U20)

Related Items

The Inverse Scattering Transform for the Defocusing Nonlinear Schrödinger Equations with Nonzero Boundary Conditions ⋮ Characterization of scattering data for the AKNS system ⋮ From the AKNS system to the matrix Schrödinger equation with vanishing potentials: Direct and inverse problems ⋮ Inverse scattering transform and soliton solutions for square matrix nonlinear Schrödinger equations with non-zero boundary conditions ⋮ The integrable property of a higher-order Zakharov-Shabat hierarchy ⋮ On the Spectrum of the Dirac Operator and the Existence of Discrete Eigenvalues for the Defocusing Nonlinear Schrödinger Equation ⋮ Direct scattering of AKNS systems with \(L^2\) potentials

Cites Work

• Scattering operators for matrix Zakharov-Shabat systems
• Semigroups of linear operators and applications to partial differential equations
• Direct and inverse scattering for selfadjoint Hamiltonian systems on the line
• On the propagation of nonlinear solitary waves in a distributed Schottky barrier diode transmission line
• Current trends in operator theory and its applications. Proceedings of the international workshop on operator theory and its applications (IWOTA), Virginia Tech, Blacksburg, VA, USA, August 6--9, 2002
• Remarks on the eigenvalues of the Manakov system
• Wave operators and similarity for some non-selfadjoint operators
• Coupling constant behavior of eigenvalues of Zakharov-Shabat systems
• The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems
• On the Eigenvalues of Zakharov--Shabat Systems
• Smooth operators and commutators
• One-dimensional dislocations. I. Static theory
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