2017/08/30 by Dan Dai, Dai, Dan, Weiying Hu +1
Mathematics · Physics and Astronomy · #33E17 #34M55 #Advanced Differential Equations and Dynamical Systems #Advanced Mathematical Physics Problems #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.1708.09357
openalex publication_date 2017/08/30 · openalex created_date 2017/09/15 · openalex updated_date 2026/07/28
We consider the quasi-Ablowitz-Segur and quasi-Hastings-McLeod solutions of the inhomogeneous Painlevé II equation u"(x)=2u3(x)+xu(x)-α \textrmfor α∈ ℝ \textrm and |α| gt; (1)/(2). These solutions are obtained from the classical Ablowitz-Segur and Hastings-McLeod solutions via the Bäcklund transformation, and satisfy the same asymptotic behaviors when x → ± ∞. For |α| > 1/2, we show that the quasi-Ablowitz-Segur and quasi-Hastings-McLeod solutions possess [ |α| + (1)/(2) ] simple poles on the real axis, which rigorously justifies the numerical results in Fornberg and Weideman (Found. Comput. Math., 14 (2014), no. 5, 985-1016).