Numerical Approach to Painlevé Transcendents on Unbounded Domains
Provides a numerical tool for studying Painlevé transcendents, which are important in mathematical physics and integrable systems.
The paper presents a multidomain spectral method for computing Painlevé transcendents on unbounded domains, avoiding truncation of asymptotic series. The method's accuracy is demonstrated on the tritronquée solution of Painlevé I.
A multidomain spectral approach for Painlevé transcendents on unbounded domains is presented. This method is designed to study solutions determined uniquely by a, possibly divergent, asymptotic series valid near infinity in a sector and approximates the solution on straight lines lying entirely within said sector without the need of evaluating truncations of the series at any finite point. The accuracy of the method is illustrated for the example of the tritronquée solution to the Painlevé I equation.