Abstract
In this paper we consider the matrix non-selfadjoint equations of the Dirac type with the corresponding boundary condition atx= 0. We investigate the connection between the spectrum of the equation and the singularities of the corresponding Weyl-Titchmarsh matrix function. Using the Weyl-Titchmarsh matrix function, we construct the Green matrix function.
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References
Ablowitz, M.J. and Segur, H.Solitons and the Inverse Scattering TransformSIAM, Philadelphia, 1981.
Bronski, J.C., Semiclassical Eigenvalue Distribution of the Zakharov-Shabat Eigen-value ProblemPhysicaD97 (1996) 376–397.
Bullough, R.K. and Caudrei, P.J. (eds.)Solitons, Topics in Current PhysicsSpringer-Verlag, 1980.
Gohberg, I., On linear operators analytically depending on a parameterDokl. Akad. Nauk SSSR78, No. 4 (1951) 629–631 (Russian).
Hille, E.Lectures on Ordinary Differential EquationsAddison-Wesley, 1969.
Hinton, D.B. and Shaw, J.K., Hamiltonian Systems of Limit Point or Limit Circle Type with Both Endpoints SingularJournal of Differential Equations30 (1983) 444–464.
Li, Y. and McLaughlin, D.W., Morse and Melnikov Functions for NLS PDE’sComm. Math. Phys.162, (1994) 175–214.
Marchenko, V.A.Sturm-Lionville Operators and ApplicationsBirkhäuser, Basel, (1986).
Sakhnovich, A.L., Nonlinear Schrödinger Equation on Semi-Axis and Inverse Problem Associated with itUkrainskii Math. Zhurnal42, No. 3, (1990) 356–363 (Russian).
Sakhnovich, L.A.Spectral Theory of Canonical Differential Systems. Method of Operator IdentitiesOperator Theory, Adv. and Appl., 107, Birkhäauser, (1999).
Sakhnovich, L.A., Spectral Analysis of Volterra Operators Given in the space Lam (, P)Ukrainskii Math. Zhurnal 2 (1964), 259–268 (Russian).
Sakhnovich, L.A., Weyl-Titchmarsh Matrix Functions for Matrix Dirac Type Equations (non-selfadjoint case)Inverse Problems18, (2002), 1525–1536.
Tkachenko, V., Non-selfadjoint Dirac operators with finite-band spectraIntegral Equations and Operator Theory36, No.3, (2000) 325–348.
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Sakhnovich, L. (2010). Weyl-Titchmarsh Matrix Functions and Spectrum of Non-selfadjoint Dirac Type Equation. In: Ball, J.A., Helton, J.W., Klaus, M., Rodman, L. (eds) Current Trends in Operator Theory and its Applications. Operator Theory: Advances and Applications, vol 149. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7881-4_24
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DOI: https://doi.org/10.1007/978-3-0348-7881-4_24
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9608-5
Online ISBN: 978-3-0348-7881-4
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