Abstract
In this paper, a more general form of unstable nonlinear Schrödinger equation which describe the time evolution of disturbances in marginally stable or unstable media is studied. A new modification of the Sardar sub-equation method is discussed and employed to retrieve solitons and other solutions of the suggested nonlinear model. A variety of solutions, including bright solitons, dark solitons, singular solitons, combo bright-singular solitons, periodic, exponential, and rational solutions are provided with considerable physical perspective. Using the q-homotopy analysis algorithm in combination with the Laplace transform, we present the approximate solutions of the bright and dark solitons, including the physical nature of the attained solutions. The computation complexity and results indicate that the given techniques are simple, effective, uncomplicated, and that they may be used to a wide range of unstable and stable nonlinear evolution equations encountered in mathematics, mathematical physics, and other applied disciplines.
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