Study of modulation instability and geometric structures of multisolitons in a medium with high dispersivity and nonlinearity

Highly dispersive and nonlinear Shrödinger equations (HDNLSEs), with seven degree nonlinearity and six-order dispersion are relevant to study the propagation of optical waves in optical fibres (OFs). Here, the model equation considered was derived very recently by Biswas and Arshed. HDNLSEs have been widely studied in many research works. In some of these works, the solutions obtained are mainly singular. Here, we are concerned with the non-singular (physical) solutions. The objective of this work is to show that the propagation of optical pulses (OPs) in OF may be in different geometric structures. The physical parameters, intensity, frequency, phase, polarisation and spectral content are introduced and investigated. A new transformation to inspect the waves produced by soliton–periodic wave collisions is suggested. Exact solutions are found by using the unified method. Numerical evaluations of these solutions are carried out. The results show different geometrical structures of solitons which are, chirped, conoidal, lumps, M-shaped and tunable solitons. These solutions show that the coefficient of the highest nonlineartity and highest order derivative terms play a dominant role. The results found here are of great interest to experiment the effects of high dispersivity and nonlinearity on OPs configuration. It is found that the equilibrium states are bistable. Furthermore, the modulation instability is analysed.