Propagation of optical soliton in a multicomponent nonlinear medium

We consider the propagation of ultrashort pulses in a multicomponent nonlinear medium by studying the evolution of an optical field in Josephson superconducting planar structures. This structure has a nonlinear dielectric barrier encompassing resonance and non-resonance nonlinearity. The formation of optical solitons in the model is possible only if a certain relation exists between the propagating pulse frequency and the components that characterize the nonlinear medium. These relations are obtained by constructing the Lax pair and it is found that the obtained conditions coincide with the integrability conditions obtained from Painlevé analysis. The conditions obtained for the existence of soliton solutions in a multicomponent medium are sufficiently enough as they characterize both linear and nonlinear properties of the medium. The one-soliton solution is obtained by Bäcklund Transformation method.