ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

Geometric series

Newton’s method of constructing exact solutions to nonlinear differential equations and non-integrable evolution equations

A modification of the Newton’s power series method for solving nonlinear ordinary equa- tions and non-integrable evolution equations is proposed. In the first stage of the method the first few terms of a power series for the sought dependent variable are determined. For this we use either the direct power series expansion in independent variable, followed by substitution into the equation, or the decomposition into functional series of perturbation method in powers of the formal parameter.