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Browsing by Subject "Riemann-Hilbert problem"
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Item Certain Aspects of Quantum and Classical Integrable Systems(2022-08) Kosmakov, Maksim; Tarasov, Vitaly; Its, Alexander; Mukhin, Evgeny; Ramras, DanielWe 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.Item 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 ScienceIn 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], 0Item Riemann–Hilbert approach to the elastodynamic equation: half plane(Springer, 2021-05) Its, Alexander; Its, Elizabeth; Mathematical Sciences, School of ScienceWe 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.