In this paper, we apply the $\tan(\circleddash/2)$ expansion and the Kudryashov general approaches to the time fractional perturbed Radhakrishnan-Kundu -Lakshmanan (RKL) equation. These integration schemes provide a number of optical soliton solutions of the model. The solutions registered with constraint conditions on the parameters that follow their existence criteria. To the constraint conditions, the solutions offer various transmission signals through optical fibres, such as double periodic optical solitons, combo optical periodic and rogue waves, combo periodic and shock waves, combo periodic and solitons, and combo double singular solitons. Moreover, after interaction of rogue and periodic waves, it is shown that the rogue waves are going to diminish after a certain time keeping periodic nature of the interaction. In fact, interaction of periodic and rogue waves produces periodic rogue type breather waves, that indicates the amplitude of the rogue waves gradually decreases, and vanishes after a certain time. Some dynamical signals are plotted in the graphs by picking suitable values on the parameters.
In this article, we study two extended higher-order KdV-type models, namely, the extended Sawada-Kotera (eSK) and the extended Lax (eLax) equations. These models successfully describe propagation of dimly nonlinear long waves in fluids, ion-acoustic waves in harmonic sparklers. We firstly derive multi-soliton solutions of the models. We then construct interection solutions in-terms of hyperbolic and sinusoidal functions using the multi-soliton solutions with appropriate complex conjugate parameters. Such parameters influence and control the phase shifts, propagation direction and energies of the waves. In particularly, we present their collision solutions in the identical plane with different parametric constraints, which degenerate to the line rogue waves, x-shaped rogue waves, cnoidal periodic waves, interactions of rogue and bell waves, line breather and double breather waves. The dynamical characteristics of the wave solutions has been plotted by choosing particular values of the parameters in graphically.