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1990•Progress of Theoretical PhysicsOpen access

Painleve Property and Algebraic Integrability of Single Variable Ordinary Differential Equations with Dominants

Masaharu Ishii

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Abstract

We consider n-th order single variable ordinary differential equations which are expressed by unx-λ(u, ux,…, u(n-1)x)=0 where λ are polynomials. Then we prove by an algebraic method that these differential equations satisfy Painlevé property's necessary condition if they have enough algebraic first integrals and dominants.

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We consider n-th order single variable ordinary differential equations which are expressed by unx-λ(u, ux,…, u(n-1)x)=0 where λ are polynomials. Then we prove by an algebraic method that these differential equations satisfy Painlevé property's necessary condition if they have enough algebraic first integrals and dominants.

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Available abstract

We consider n-th order single variable ordinary differential equations which are expressed by unx-λ(u, ux,…, u(n-1)x)=0 where λ are polynomials. Then we prove by an algebraic method that these differential equations satisfy Painlevé property's necessary condition if they have enough algebraic first integrals and dominants.

Key concepts: Property (philosophy), Variable (mathematics), Ordinary differential equation, Differential algebraic equation, Algebraic number, Differential algebraic geometry, Differential equation, Differential (mechanical device)

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