Abstract
Raman effect is due to self-phase modulation (SPM), which is embedded in Kundu--Eckhaus equation KEE. Here, the objective of this work is to present a generalized KEE by accounting for an extra dispersion which may be induced by Raman scattering. Also, attention is focused to study the effects of the extra dispersion.Which are investigated via obtaining the exact solutions of the new model equation. These solutions are found by the unified method and by introducing a new transformation that ispects soliton- periodic wave collision. We aim to show that a variety of shapes of optical pulses OPs propagation in optical fibers occurs. Waves of multiple geometric structures are observed. Among these waves, hybrid lumps, soliton, cascade, complex chirped, hybrid w-shaped, rhombus (diamond) waves and soliton self phase modulation.The characteristics of the pulses; intensity, frequency, wavelength, polarization, and spectral content are identified. The results found here are of great interest in experimenting the effects of the induced dispersion on pulses configurations. Further, the colliding dynamics are inspected and as it is observed that no rogue or sharp waves formation hold, so the collision is elastic.
Highlights
Nonlinear Schrodinger equations NLSEs were the objective of huge number of research works in the literature
It was found that NLSEs possess an infinite number of conservation laws [6]
Which is due to self-phase modulation (SPM) which may lead to an extra dispersion
Summary
Nonlinear Schrodinger equations NLSEs were the objective of huge number of research works in the literature. NLSEs may have a diversity of forms They can taken to describe optical wave propagation in highly dispersive medium. The effect of self-phase modulation of a pulse propagation was analyzed in [10]. The KEE .is a NLSE with Raman effect It occupied a wide area of research in the literature [12,13,14,15,16,17,18,19,20,21]. In [17], new complex analytical solutions in weakly nonlinear dispersive medium, by using an improved Bernoulli sub-equation method, was derived. We are concerned of studying the behavior of solutions of the KEE with an extra dispersion.The unified method is used to find the exact solutions [25,26,27,28,29]
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