Painleve property and the first integrals of nonlinear differential equations

Details Painleve property and the first integrals of nonlinear differential equations Painleve property and the first integrals of nonlinear differential equations

2004-08-23

arxiv.org/abs/nlin/0408041v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

22 pages

Scientific paper

Link between the Painleve property and the first integrals of nonlinear ordinary differential equations in polynomial form is discussed. The form of the first integrals of the nonlinear differential equations is shown to determine by the values of the Fuchs indices. Taking this idea into consideration we present the algorithm to look for the first integrals of the nonlinear differential equations in the polynomial form. The first integrals of five nonlinear ordinary differential equations are found. The general solution of one of the fourth ordinary differential equations is given.

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