Kuznetsov–Ma waves train generation in a left-handed material

Abstract

We analyze the behavior of an electromagnetic wave which propagates in a left-handed material. Second-order dispersion and cubic–quintic nonlinearities are considered. This behavior of an electromagnetic wave is modeled by a nonlinear Schrödinger equation which is solved by collective coordinates theory in order to characterize the light pulse intensity profile. More so, a specific frequency range has been outlined where electromagnetic wave behavior will be investigated. The perfect combination of second-order dispersion and cubic nonlinearity leads to a robust soliton. When the quintic nonlinearity comes into play, it provokes strong and long internal perturbations which lead to Benjamin–Feir instability. This phenomenon, also called modulational instability, induces appearance of a Kuznetsov–Ma waves train. We numerically verify the validity of Kuznetsov–Ma theory by presenting physical conditions which lead to Kuznetsov–Ma waves train generation. Thereafter, some properties of such waves train are also verified.