2018/08/27 by Piotr Kokocki, Kokocki, Piotr
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Algebraic structures and combinatorial models #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.1808.09039
openalex publication_date 2018/08/27 · openalex created_date 2022/08/03 · openalex updated_date 2026/07/28
In this paper, we establish a formula determining the value of the Cauchy\nintegrals of the real and purely imaginary Ablowitz-Segur solutions for the\ninhomogeneous second Painlev 'e equation. Our approach relies on the analysis\nof the corresponding Riemann-Hilbert problem and the construction of an\nappropriate parametrix in a neighborhood of the origin. Obtained integral\nformulas are consistent with already known analogous results for Ablowitz-Segur\nsolutions of homogeneous Painlev 'e II equation.\n