Abstract
The present paper investigates the features of specific waves in a weakly nonlocal nonlinear medium. More precisely, a generalized nonlinear Schrödinger equation (gNLSE) involving a high-order dispersion term, a high-order nonlinear term, and the effect of a term that accounts for the weak nonlocality is considered. By applying the Jacobi elliptic function (JEF) method, a wide range of Jacobi elliptic function solutions to the governing model is first derived. The characteristics of modulation instability (MI) and modulated wave (MW) topological and non-topological solitons are then analyzed by giving a series of two- and three-dimensional graphs. A major accomplishment of the study is the discovery of stable and unstable zones, as well as the control of the amplitude of topological and non-topological solitons.
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