Abstract

In this article, the modified direct algebraic method is applied for the perturbed nonlinear Schrödinger equation (NLSE) describing the dynamics of optical solitons in metamaterials, in the presence of quadratic–cubic nonlinearity. Various types of solutions are extracted such as bright solitons, singular solitons, dark solitons, singular periodic wave solutions, periodic wave solutions, plane wave solutions, Jacobi elliptic wave solutions, exponential wave solutions, hyperbolic wave solutions and Weierstrass elliptic solutions. Moreover, for the physical illustration of the obtained solutions, 3D graphs are presented.

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