Browsing by Subject "Riemann-Hilbert problem"

Now showing 1 - 3 of 3
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    Certain Aspects of Quantum and Classical Integrable Systems
    (2022-08) Kosmakov, Maksim; Tarasov, Vitaly; Its, Alexander; Mukhin, Evgeny; Ramras, Daniel
    We derive new combinatorail formulas for vector-valued weight functions for the evolution modules over the Yangians Y (gl_n). We obtain them using the Nested Algebraic Bethe ansatz method. We also describe the asymptotic behavior of the radial solutions of the negative tt* equation via the Riemann-Hilbert problem and the Deift-Zhou nonlinear steepest descent method.
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    A Riemann-Hilbert Approach to Asymptotic Analysis of Toeplitz+Hankel Determinants
    (SIGMA. Symmetry, Integrability and Geometry: Methods and Applications, 2020-10-06) Gharakhloo, Roozbeh; Its, Alexander; Mathematical Sciences, School of Science
    In this paper we will formulate 4×4 Riemann-Hilbert problems for Toeplitz+Hankel determinants and the associated system of orthogonal polynomials, when the Hankel symbol is supported on the unit circle and also when it is supported on an interval [a,b], 0
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    Riemann–Hilbert approach to the elastodynamic equation: half plane
    (Springer, 2021-05) Its, Alexander; Its, Elizabeth; Mathematical Sciences, School of Science
    We show, how the Riemann–Hilbert approach to the elastodynamic equations, which have been suggested in our preceding papers, works in the half plane case. We pay a special attention to the emergence of the Rayleigh waves within the scheme.