Existence of second order solitary solutions to Riccati differential equations coupled with a multiplicative term

The construction of the second order solitary solutions to two Riccati differential equations coupled with a multiplicative term is discussed in this paper. The generalized differential operator method is used to derive necessary and sufficient conditions for the existence of these solutions in the space of system’s parameters and initial conditions. The method does not need linearization, weak nonlinearity assumptions or perturbation theory. Computational experiments illustrate the complexity of dynamical processes in nonlinear differential equations coupled with a multiplicative term.