Mixed problem for a nonlinear system of equations of Schrödinger type
The author investigates an initial-boundary value problem for three partial differential equations describing three-particle interaction of electromagnetic waves in a nonlinear medium for the planar case. This system can be written in the form \[ \partial u/\partial t=A(\partial u/\partial x)+B(\partial^ 2u/\partial x^ 2)+C(u) \] for (x,t)\(\in (0,1)\times (0,T)\). A and B are diagonal matrices, and C is a special nonlinear function of u. It is established that under proper initial and boundary conditions a unique solution exists in suitable function spaces.
scientific article; zbMATH DE number 4017479