On the location of poles for the Ablowitz-Segur family of solutions to   the second Painlev\'e equation
  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. 
Marco Bertola
nlin.SI math.CA