Formation of solitons with shape changing for a generalized nonlinear Schrödinger equation in an optical fiber

In optical fibers, the generalized nonlinear Schrödinger equations with self-steepening (SS), self-frequency shift (SFS), intermodal dispersion (IMD), and third-order dispersion (TOD) play an important role. Our investigation covers a variety of physical parameters based on how optical solitons change their structure as they move through an optical medium. Our study shows that modifying the coefficients for SS, SFS, IMD, and TOD can affect optical solitons’ profiles either by altering their nature or without doing so. We used the extended rational sinh–cosh method, which works with various types of soliton profiles. These profiles include dark, kink-dark, kink, and anti-kink solitons. By selecting appropriate physical parameter values, the behavior of various optical solitons is graphically depicted. As a result, we utilize the eigenvalue spectrum to investigate linear stability analysis.