On the quasi-Ablowitz–Segur and quasi-Hastings–McLeod solutions of the inhomogeneous Painlevé II equation
Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review
Author(s)
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Detail(s)
| Original language | English |
|---|---|
| Article number | 1840004 |
| Journal / Publication | Random Matrices: Theory and Application |
| Volume | 7 |
| Issue number | 4 |
| Online published | 28 Feb 2018 |
| Publication status | Published - Oct 2018 |
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Abstract
We consider the quasi-Ablowitz–Segur and quasi-Hastings–McLeod solutions of the inhomogeneous Painlevé II equation
u′′(x) = 2u3(x) + xu(x) − α for α ∈ R and ∣α∣ >1/2.
These solutions are obtained from the classical Ablowitz–Segur (AS) and Hastings–McLeod (HM) solutions via the Bäcklund transformation, and satisfy the same asymptotic behaviors when x → ±∞. For |α| > 1/2, we show that the quasi-Ablowitz–Segur (qAS) and quasi-Hastings–McLeod (qHM) solutions possess [∣α∣ + 1/2] simple poles on the real axis, which rigorously justifies the numerical results in Fornberg and Weideman (A computational exploration of the second Painlevé equation, Found. Comput. Math. 14(5) (2014) 985–1016).
u′′(x) = 2u3(x) + xu(x) − α for α ∈ R and ∣α∣ >1/2.
These solutions are obtained from the classical Ablowitz–Segur (AS) and Hastings–McLeod (HM) solutions via the Bäcklund transformation, and satisfy the same asymptotic behaviors when x → ±∞. For |α| > 1/2, we show that the quasi-Ablowitz–Segur (qAS) and quasi-Hastings–McLeod (qHM) solutions possess [∣α∣ + 1/2] simple poles on the real axis, which rigorously justifies the numerical results in Fornberg and Weideman (A computational exploration of the second Painlevé equation, Found. Comput. Math. 14(5) (2014) 985–1016).
Research Area(s)
- Ablowitz–Segur solutions, Bäcklund transformation, Hastings–McLeod solutions, Painlevé II equation
Citation Format(s)
On the quasi-Ablowitz–Segur and quasi-Hastings–McLeod solutions of the inhomogeneous Painlevé II equation. / Dai, Dan; Hu, Weiying.
In: Random Matrices: Theory and Application, Vol. 7, No. 4, 1840004, 10.2018.
In: Random Matrices: Theory and Application, Vol. 7, No. 4, 1840004, 10.2018.
Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review
