Optical solitons and stability analysis for the generalized second-order nonlinear Schrödinger equation in an optical fiber

In this paper, the generalized second-order nonlinear Schrödinger equation with light-wave promulgation in an optical fiber, is studied for optical soliton solutions. Three analytical methods such as the <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi>exp</m:mi> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mo>−</m:mo> <m:mi>ϕ</m:mi> <m:mrow> <m:mo>(</m:mo> <m:mi>χ</m:mi> <m:mo>)</m:mo> </m:mrow> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:mrow> </m:math> exp(-φ (χ )) -expansion method, the G ′/ G 2 -expansion method and the first integral methods are used to extract dark, singular, periodic, dark-singular combo optical solitons for the proposed model. These solitons appear with constraint conditions on their parameters and they are also presented. These three strategic schemes have made this retrieval successful. The given model is also studied for modulation instability on the basis of linear stability analysis. A dispersion relation is obtained between wave number and frequency.