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.

KEYWORDS:

• Extended complex backward–forward derivative operator
• nonlinear wave equations

Acknowledgements

The author would like to thank the anonymous referees for their useful comments and valuable suggestions.

Disclosure statement

No potential conflict of interest was reported by the author.