Cubic�quartic optical solitons in Lakshmanan�Porsezian�Daniel model derived with semi-inverse variational principle

Abstract

We retrieve analytically a bright 1-soliton solution to a perturbed cubic−quartic Lakshmanan-Porsezian-Daniel model, using a semi-inverse variational principle. The perturbation terms are considered arising from the condition of maximum allowable intensity. The restrictions imposed by integrability considerations on the model parameters are enlisted. It is important that the other analytical approaches available fail to recover the analytical bright-soliton solution to the model with the maximum allowable intensity.

Interacting Solitons, Periodic Waves and Breather for Modified Korteweg–de Vries Equation

“…It is also relevant to mention that the functional form of the interacting periodic wave and breathers wave solutions (15) and ( 20) are also different from those obtained very recently by Ma and Li [47] and previously by Kevrekidis et al [32] as well as Alejo and Muñoz. [48] This illustrates the richness of nonlinear systems modeled by the mKdV equation, which is often measured by the variety of wave structures that the medium can support.…”

“…Additionally, we have found that the existence of these new structures depend drastically on the type of nonlinearity of the nonlinear medium (a self-focusing or defocusing one). These results constitute the analytical demonstration of existence of new closed form solutions in the form of a pair interacting solitons (10), interacting periodic waves (15) and breathers waves (20) to the mKdV equation. The wide applicability of the mKdV equation to describe evolution dynamics of nonlinear waves in a variety of different physical media allows the usefulness of our results to recognize various nonlinear phenomena and dynamical processes in these systems.…”

“…It is worth mentioning that the inclusion of the joint parameter 𝑠 makes the obtained solution (10) more general in the sense that every solution is determined for each value of this parameter. Moreover, the new interacting periodic wave and breather wave solutions (15) and (20) obtained here for the mKdV model are firstly presented in this study. We note that our solutions are also general in a mathematical sense, as they are obtained without assuming parametric conditions for their existence.…”

“…This trend is very commonly visible in various equations that are visible in nonlinear optics. [13][14][15] An example of these evolution models is the modified Korteweg-de Vries (mKdV) equation which has been demonstrated to describe the evolution of long waves in the critical case of vanishing quadratic nonlinearity. [16] Particularly, this equation is relevant for nonlinear waves in distributed Schottky barrier diode transmission lines [17] and internal waves in stratified fluids.…”

“…Thus the exact solutions ( 10), (15), and ( 20) to the mKdV equation with the focusing and defocusing types of nonlinearity are obtained via the inverse-scattering transform. Moreover, one may conclude that a physical system described by the mKdV equation could allow a breather evolution in either the focusing or the defocusing nonlinearity.…”