Efficient algorithms for solving the spectral scattering problems\\ for the Manakov system of nonlinear Schroedinger equations
``Vectorial'' numerical algorithms are proposed for solving the inverse and direct spectral scattering problems for the nonlinear vector Schroedinger equation, taking into account wave polarization, known as the Manakov system. It is shown that a new algebraic group of 4-block matrices wit...
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Main Author | |
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Format | Journal Article |
Language | English |
Published |
05.06.2020
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Subjects | |
Online Access | Get full text |
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Summary: | ``Vectorial'' numerical algorithms are proposed for solving the inverse and
direct spectral scattering problems for the nonlinear vector Schroedinger
equation, taking into account wave polarization, known as the Manakov system.
It is shown that a new algebraic group of 4-block matrices with off-diagonal
blocks consisting of special vector-like matrices makes possible the
generalization of numerical algorithms of the scalar problem to the vector
case, both for the focusing and defocusing Manakov systems. As in the scalar
case, the solution of the inverse scattering problem consists of inversion of
matrices of the discretized system of Gelfand-Levitan-Marchenko integral
equations using the Toeplitz Inner Bordering algorithm of Levinson's type. Also
similar to the scalar case, the algorithm for solving the direct scattering
problem obtained by inversion of steps of the algorithm for the inverse
scattering problem. Testing of the vector algorithms performed by comparing the
results of the calculations with the known exact analytical solution (the
Manakov vector soliton) confirmed the numerical efficiency of the vector
algorithms. |
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DOI: | 10.48550/arxiv.2006.03770 |