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Nonlinear wave equations from a non-local complex backward–forward derivative operator

ABSTRACT In this study, we argue that it is possible to construct non-local nonlinear wave equations with random propagation as extensions to some well-known wave equations found in field theory with cubic interactions like Maxwell–Klein–Gordon equations, Dirac–Klein–Gordon equations, wave maps, solitons and Yang–Mills equations. Our construction is based on the extended complex backward–forward derivative operator which represents the basic differentiable operator tool to deal with non-local Lagrangians.