Abundant families of Jacobi elliptic function solutions and peculiar dynamical behavior for a generalized derivative nonlinear Schrödinger equation employing extended F-expansion method

Abstract This study investigates a generalized derivative nonlinear Schrödinger (GDNLS) equation , demonstrating how ultrashort pulses propagate in a single-mode optical fiber. The extended F-expansion method, which is a modification of Kudryashov’s auxiliary equation approach, is applied in this investigation to generate Jacobi elliptic solutions for the GDNLS. Three distinct solution instances are examined, and a variety of explicit solutions, including breathers, solitary waves, bright/dark solitons, bright-dark interaction solitons, a soliton-like solution, and a rogue-like solution, are obtained. To demonstrate the complex dynamical behavior of GDNLS equation, several representative solutions are chosen and their moduli are shown in three-dimensional, two-dimensional, and contour plots using Maple software.