Existence of solitary solutions in a class of nonlinear differential equations with polynomial nonlinearity

The inverse balancing method for the determination of the necessary conditions of existence of solitary solutions to mth order differential equations with nth order polynomial nonlinearity is presented in this paper. It is shown that the order of possible solitary solutions does not increase if orders of the differential equation and the polynomial nonlinearity increase. Furthermore, the relationships between the order of the solitary solution and the order of the equation (and the nonlinearity) are given in the explicit form.