A computational overview of the solution space of the imaginary Painleve II equation

作者：Fornberg Bengt; Weideman J A C^*

来源：Physica D: Nonlinear Phenomena , 2015, 309: 108-118.

DOI：10.1016/j.physd.2015.07.008

• Imaginary Painleve II
• Modified Painleve II
• Ablowitz-Segur solutions
• Tronquee solutions
• Pole field solver

The six Painleve equations were first formulated about a century ago. Since the 1970s, it has become increasingly recognized that they play a fundamental role in a wide range of physical applications. A recently developed numerical pole field solver (Fornberg and Weideman, 2011) now allows their complete solutions spaces to be surveyed across the complex plane. Following such surveys of the P-I, P-II and P-IV equations, we consider here the case of the imaginary P-II equation (the standard P-II equation, with a change of sign for its nonlinear term). Solutions to this equation share many features with other classes of Painleve transcendents, including a rich variety of pole field configurations, with connection formulas linking asymptotic behaviors in different directions of the complex plane.

• 出版日期2015-8-1