Existence of solitary solutions in systems of PDEs with multiplicative polynomial coupling

Necessary conditions for the existence of solitary solutions to systems of nonlinear partial differential equations with multiplicative polynomial coupling are derived in this paper. The inverse balancing technique is used to explicitly determine necessary existence conditions in terms of orders of the system and the nonlinearity. As the orders of the system increase, the order of solitary solutions does not increase monotonically. A computational framework for the derivation of additional constraints on the parameters of higher-order solitary solutions is presented.