The Direct Monodromy Problem of Painleve-I
Davide Masoero
TL;DR
This paper presents a novel algorithm for solving the direct monodromy problem of Painleve-I by leveraging Nevanlinna's geometric theory of Schrödinger equations, enhancing computational approaches in integrable systems.
Contribution
It introduces a new algorithm based on Nevanlinna's geometric theory for computing monodromy data of Painleve-I's associated Schrödinger equation.
Findings
The algorithm effectively computes monodromy data for Painleve-I.
It provides a new computational tool for isomonodromic deformation problems.
The approach improves accuracy and efficiency over previous methods.
Abstract
The Painleve first equation can be represented as the equation of isomonodromic deformation of a Schrodinger equation with a cubic potential. We introduce a new algorithm for computing the direct monodromy problem for this Schrodinger equation. The algorithm is based on the geometric theory of Schrodinger equation due to Nevanlinna
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Taxonomy
TopicsNonlinear Waves and Solitons · Numerical methods for differential equations · Mathematical functions and polynomials