Quantization and soliton-like solutions for the $$\Phi \Psi $$-model in an optic fiber

Abstract In the framework of a mesoscopical model for dielectric media we provide an analytical description electromagnetic field confined in cylindrical cavity containing finite sample. This system is apted to simulate optic fiber, which two different regions, vacuum region and one, appear. A complete scattering basis introduced, together with quantization two-point function. Furthermore, also determine soliton-like solutions dielectric, propagating sample nonlinear medium.