Nonlinear coupled wave propagation in a n-dimensional layer

The paper focuses on the generalization of a nonlinear multi-parameter eigenvalue problem for a system of nonlinear differential equations. The problem is reduced to a system of nonlinear integral equations on a segment. The notion of eigentuple is introduced, the existence of a finite number of isolated eigentuples is proved, and their distribution is described. The corresponding linear multi-parameter eigenvalue problem is studied as well; it is proved that the linear problem has an infinite number of isolated eigentuples. Applications to nonlinear electromagnetic wave propagation theory are demonstrated.