2017
Том 69
№ 9

All Issues

On an integral manifold of nonlinear differential equations containing slow and fast motions

Lykova O. B., Mitropolskiy Yu. A.

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Abstract

The authors establish the existence and properties of an $s + 1$ -dimensional local integral manifold of a system of $l + m + n$ nonlinear differential equations of the form $$\frac{dx}{dt} = X(y,z)x + \varepsilon X_1(t, x, y, z),$$ $$\frac{dy}{dt} =Y(x, z), y + \varepsilon Y_1 (t, x, y, z),$$ $$\frac{dz}{dt} = \varepsilon Z_1 (t, x, y, z),$$ where $x, y$ characterize the fast, and $z$ the slow motions.

Citation Example: Lykova O. B., Mitropolskiy Yu. A. On an integral manifold of nonlinear differential equations containing slow and fast motions // Ukr. Mat. Zh. - 1964. - 16, № 2. - pp. 157-163.

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