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

Abstract

Using a simple operator-norm estimate we show that the solution to the second Painlevé 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.

8 pages, to appear in Nonlinearity

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