Bifurcation analysis and multi-stability of chirped form optical solitons with phase portrait

Abstract

As a result of oversimplified anti-cubic non-linearity, we are interested in form optical solitons to the nonlinear Schrödinger equation (NLSE). The modified G′G2 creates new solitons that include periodic type solitons in chirped forms. These findings are extremely beneficial to the study of optics. The acquired outcomes are confirmed and explained using various graphs. Computational results show that the preceding analytical expansion scheme is efficient. We present some sufficient conditions for the presence of random quasi-periodic measures for various partial differential equations and sufficient conditions for the presence of quasi-periodic measurements and satisfaction of the NLSE equation. It is discovered that a saddle point bifurcation causes the transition from periodic to quasi-periodic actions in a sensitive area. Further investigation reveals favorable conditions for the multidimensional bifurcation of increasingly complex solutions. Our results provide insight into the complex interplay between periodic and quasi-periodic behaviors and further our understanding of the complex dynamics displayed by these PDE‘s. The outcomes that are being given broaden the field's current understanding and provide opportunities for more investigation into the intricate mathematical structures that underlie partial differential equation solutions.