Tree-like structures and Freak waves generation induced by quintic-nonlinearity and cubic-Raman effect in a nonlinear metamaterial

The goal of this investigation is based on electromagnetic wave behavior which is modeled by a nonlinear Schrodinger equation in a nonlinear metamaterial optical system. Two regimes are under consideration known as negative index regime and absorption regime. During the propagation, second-order dispersion, cubic-quintic nonlinearities and cubic-Raman effect are taken into account. The characterization of electromagnetic wave is assured by collective coordinates method and conventional ansatz function. The soliton light pulse is progressively modified by quintic-nonlinearity and cubic-Raman effect in order to provoke freak waves, tree structures and soliton self-frequency shift generation. Hence, the coefficients of the Schrodinger equation are plotted in order to improve the explanation of these strange phenomena. Moreover, all those above mentioned phenomena are strongly influenced by frequency and the regime under consideration. Thus, some specific freak waves such as Kuznetsov–Ma, Peregrine and Riemann waves are found. It is clearly pointed out the key role of internal and external disturbances due to cubic-Raman effects. That leads to freak waves, tree structures and soliton self frequency shift generation for both regimes. The so-called self-compensation process as technique of cancellation of these phenomena is also investigated.