Solving Nonlinear Second-Order Differential Equations through the Attached Flow Method

The paper considers a simple and well-known method for reducing the differentiability order of an ordinary differential equation, defining first derivative as function that will become new variable. Practically, we attach to initial equation supplementary one, very similar flow from dynamical systems. This is why name it “attached equation”. Despite its apparent simplicity, approach asks closer investigation because reduced in variable could be difficult integrate. To overcome this difficulty, class second-order equations, proposing decomposition free term two parts formulating rules, based on specific balancing procedure, how choose flow. These are main novelties illustrated by solving important equations theory solitons those arising Chafee–Infante, Fisher, or Benjamin–Bona–Mahony models.