Necessary and sufficient conditions for arbitrary linear combinations of solutions of a class of nonlinear partial differential equations to satisfy the differential equation

Abstract

The class of nonlinear partial differential equations that can be decomposed into sums of terms that are products of not necessarily the same number of linear differential operators is considered. Necessary and sufficient conditions for an arbitrary linear combination of a finite and an infinite number of solutions to satisfy the equation are derived. Mathematics Subject Classification: 35G20, 35G31, 35G99