Evolution of Weyl Functions and Initial-Boundary Value Problems
DOI10.1051/mmnp/201611209zbMath1385.34020arXiv1507.08796OpenAlexW1867091668MaRDI QIDQ4607490
Publication date: 14 March 2018
Published in: Mathematical Modelling of Natural Phenomena (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1507.08796
inverse probleminitial-boundary value problemboundary conditionscompatibility conditioninitial conditionsWeyl functionresponse functionzero curvature representationnonlinear integrable equationquasi-analytic functiondynamical Dirac systemspectral Dirac systemevolution of the Weyl function
Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Weyl theory and its generalizations for ordinary differential equations (34B20) Inverse problems involving ordinary differential equations (34A55) Research exposition (monographs, survey articles) pertaining to ordinary differential equations (34-02) Initial-boundary value problems for systems of nonlinear higher-order PDEs (35G61) Initial-boundary value problems for systems of nonlinear first-order PDEs (35F61) Overdetermined initial-boundary value problems for PDEs and systems of PDEs (35N30) Initial-boundary value problems for systems of linear first-order PDEs (35F46)
Cites Work
- Singular Weyl-Titchmarsh-Kodaira theory for one-dimensional Dirac operators
- Inverse problems and nonlinear evolution equations. Solutions, Darboux matrices and Weyl-Titchmarsh functions
- Quantum complex sine-Gordon model on a half line
- Nonlinear Schrödinger equation in a semi-strip: evolution of the Weyl-Titchmarsh function and recovery of the initial condition and rectangular matrix solutions from the boundary conditions
- Inverse spectral problems for Dirac operators on a finite interval
- On the compatibility condition for linear systems and a factorization formula for wave functions
- Inverse problem for Dirac systems with locally square-summable potentials and rectangular Weyl functions
- Expansion of functions of quasianalytic classes in series of polynomials
- Hamiltonian methods in the theory of solitons. Transl. from the Russian by A. G. Reyman
- Initial value problems for integrable systems on a semi-strip
- Nonlinear Schrödinger equation on a semi-axis and an inverse problem associated with it
- The boundary control approach to the Titchmarsh-Weyl \(m\)-function. I: The response operator and the \(A\)-amplitude
- Theory of group representations and integration of nonlinear systems \(x_{a, z\overline{z}}=\exp(kx)_{a}\)
- Integration of nonlinear equations of mathematical physics by the method of inverse scattering. II
- The collected works of Arne Beurling. Volume 1: Complex analysis. Volume 2: Harmonic analysis. Ed. by Lennart Carleson, Paul Malliavin, John Neuberger, John Wermer
- The periodic problem for the Korteweg-de Vries equation
- Spectral theory of canonical differential systems. Method of operator identities
- The Goursat problem for the sine-Gordon equation and the inverse spectral problem
- A new approach to inverse spectral theory. II: General real potentials and the connection to the spectral measure
- Integrable Hamiltonian systems and interactions through quadratic constraints
- Integrable nonlinear evolution equations on the half-line
- Abstract wave equations and associated Dirac-type operators
- Skew-self-adjoint Dirac system with a rectangular matrix potential: Weyl theory, direct and inverse problems
- Supersymmetry and Schrödinger-type operators with distributional matrix-valued potentials
- Inverse spectral problems for Schrödinger-type operators with distributional matrix-valued potentials.
- Reconstruction of radial Dirac and Schrödinger operators from two spectra
- Trace formulas and Borg-type theorems for matrix-valued Jacobi and Dirac finite difference operators
- KdV Equation in the Quarter–Plane: Evolution of the Weyl Functions and Unbounded Solutions
- Boundary Control Method in Dynamical Inverse Problems — An Introductory Course
- Inverse problem for a one-dimensional dynamical Dirac system (BC-method)
- TheN-wave problem on the half-line
- Commutation Methods Applied to the mKdV-Equation
- Dynamical and spectral Dirac systems: response function and inverse problems
- WAVE BASES IN MULTIDIMENSIONAL INVERSE PROBLEMS
- A Unified Approach to Boundary Value Problems
- Initial-boundary-value problems for linear and integrable nonlinear dispersive partial differential equations
- Scattering and inverse scattering for first order systems
- Witten index, axial anomaly, and Krein’s spectral shift function in supersymmetric quantum mechanics
- BOUNDARY CONTROL AND A MATRIX INVERSE PROBLEM FOR THE EQUATION $ u_{tt}-u_{xx}+V(x)u=0$
- A complete solution of the periodic Toda problem
- The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems
- Dirac type and canonical systems: spectral and Weyl–Titchmarsh matrix functions, direct and inverse problems
- Unified approach to strings and vortices with soliton solutions
- Second harmonic generation: Goursat problem on the semi-strip, Weyl functions and explicit solutions
- Robin boundary condition and shock problem for the focusing nonlinear Schrödinger equation
- Analyticity and uniform stability in the inverse spectral problem for Dirac operators
- Weyl theory and explicit solutions of direct and inverse problems for Dirac system with a rectangular matrix potential
- On the rigorous foundations of the Fokas method for linear elliptic partial differential equations
- Reconstructing the potential for the one-dimensional Schrodinger equation from boundary measurements
- Weyl functions, the inverse problem and special solutions for the system auxiliary to the nonlinear optics equation
- Inverse problems for the Schrödinger equation via Carleman inequalities with degenerate weights
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