dorsal/arxiv
View SchemaAsymptotic approach for the rigid condition of appearance of the oscillations in the solution of the Painleve-2 equation
| Authors | O. M. Kiselev |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9902007 |
| URL | https://arxiv.org/abs/solv-int/9902007 |
Abstract
The asymptotic solution for the Painleve-2 equation with small parameter is considered. The solution has algebraic behavior before point $t_*$ and fast oscillating behavior after the point $t_*$. In the transition layer the behavior of the asymptotic solution is more complicated. The leading term of the asymptotics satisfies the Painleve-1 equation and some elliptic equation with constant coefficients, where the solution of the Painleve-1 equation has poles. The uniform smooth asymptotics are constructed in the interval, containing the critical point $t_*$.
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"abstract": "The asymptotic solution for the Painleve-2 equation with small parameter is\nconsidered. The solution has algebraic behavior before point $t_*$ and fast\noscillating behavior after the point $t_*$. In the transition layer the\nbehavior of the asymptotic solution is more complicated. The leading term of\nthe asymptotics satisfies the Painleve-1 equation and some elliptic equation\nwith constant coefficients, where the solution of the Painleve-1 equation has\npoles. The uniform smooth asymptotics are constructed in the interval,\ncontaining the critical point $t_*$.",
"arxiv_id": "solv-int/9902007",
"authors": [
"O. M. Kiselev"
],
"categories": [
"solv-int",
"nlin.SI"
],
"title": "Asymptotic approach for the rigid condition of appearance of the oscillations in the solution of the Painleve-2 equation",
"url": "https://arxiv.org/abs/solv-int/9902007"
},
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