Painleve test and higher order differential equations
Ugurhan Mugan, Fahd Jrad
TL;DR
This paper explores higher order Painlevé-type equations derived from the second Painlevé equation through singular point analysis, expanding the understanding of integrability in nonlinear differential equations.
Contribution
It introduces a method to generate higher order Painlevé-type equations from the second Painlevé equation using singular point analysis.
Findings
Derived new higher order Painlevé-type equations
Analyzed singular points to establish integrability
Extended Painlevé classification to higher orders
Abstract
Starting from the second Painlev\'{e} equation, we obtain Painlev\'{e} type equations of higher order by using the singular point analysis.
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Taxonomy
TopicsNonlinear Waves and Solitons · Numerical methods for differential equations · Fractional Differential Equations Solutions