Investigation of solitons and conservation laws in an inhomogeneous optical fiber through a generalized derivative nonlinear Schrödinger equation with quintic nonlinearity

The current research investigates the behavior of femtosecond solitary waves in an inhomogeneous optical fiber using the generalized derivative nonlinear Schrödinger equation with quintic nonlinearity. The extended F-expansion technique is utilized to obtain various exact solutions such as bright soliton solutions, dark soliton solutions, combo bright–dark soliton solutions, singular soliton solutions, periodic solutions, Jacobi elliptic functions solutions, rational solutions, Weierstrass elliptic solutions, exponential solutions. The obtained solutions are presented in three-dimensional and contour graphics by selecting appropriate parameters. Ibragimov’s conservation technique is also applied to obtain conservation laws for the given model. These findings are crucial for comprehending various of scientific and physical applications.