On the location of poles for the Ablowitz-Segur family of solutions to the second Painlevé equation

Details On the location of poles for the Ablowitz-Segur family of solutions to the second Painlevé equation On the location of poles for the Ablowitz-Segur family of solutions to the second Painlevé equation

2012-03-14

arxiv.org/abs/1203.2988v1

Nonlinearity 25 (2012) 1179--1185

Nonlinear Sciences

Exactly Solvable and Integrable Systems

8 pages, to appear in Nonlinearity

Scientific paper

Using a simple operator-norm estimate we show that the solution to the second
Painlev\'e equation within the Ablowitz-Segur family is pole-free in a well
defined region of the complex plane of the independent variable. The result is
illustrated with several numerical examples.

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