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Spectral parameter power series representation for solutions of linear system of two first order differential equations

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  • Gutiérrez Jiménez, Nelson
  • Torba, Sergii M.

Abstract

A representation in the form of spectral parameter power series (SPPS) is given for a general solution of a one dimension Dirac system containing arbitrary matrix coefficient at the spectral parameter,BdYdx+P(x)Y=λR(x)Y,(*)where Y=(y1,y2)T is the unknown vector-function, λ is the spectral parameter, B=(01−10), and P is a symmetric 2 × 2 matrix, R is an arbitrary 2 × 2 matrix whose entries are integrable complex-valued functions. The coefficient functions in these series are obtained by recursively iterating a simple integration process, beginning with a non-vanishing solution for one particular λ=λ0. The existence of such solution is shown.

Suggested Citation

  • Gutiérrez Jiménez, Nelson & Torba, Sergii M., 2020. "Spectral parameter power series representation for solutions of linear system of two first order differential equations," Applied Mathematics and Computation, Elsevier, vol. 370(C).
    • Handle: RePEc:eee:apmaco:v:370:y:2020:i:c:s0096300319309038
    DOI: 10.1016/j.amc.2019.124911
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    References listed on IDEAS

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    1. Kravchenko, Vladislav V. & Navarro, Luis J. & Torba, Sergii M., 2017. "Representation of solutions to the one-dimensional Schrödinger equation in terms of Neumann series of Bessel functions," Applied Mathematics and Computation, Elsevier, vol. 314(C), pages 173-192.
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