Optical solitons of NLS-type differential equations by extended direct algebraic method

Abstract

In this paper, we examine the optical soliton solutions of nonlinear partial differential equations belonging to the nonlinear Schrödinger (NLS) class which includes cubic focusing NLS equation and paraxial NLS equation in a Kerr media. We construct the optical soliton of these models using a new extended direct algebraic method (NEDAM). The resulting solutions carry a variety of new families including singular solutions of Types 1 and 2, dark, darkly bright and dark singular soliton solutions. Sufficient conditions are provided for these structures to exist. NEDAM is successfully applied to supposed nonlinear model and provides us some new and interesting solitary wave solutions. These solutions contain the trigonometric-, hyperbolic- and exponential-type functions. Moreover, to present the physical importance of the considered model, some [Formula: see text] and [Formula: see text] diagrams of obtained solutions are plotted by using Mathematica under the suitable choice of involving parameters values.

Conservation Laws, Solitary Wave Solutions, and Lie Analysis for the Nonlinear Chains of Atoms

“…The Lie symmetry analysis approach [12][13][14][15][16][17][18][19][20][21][22] is a powerful method used in the study of nonlinear PDEs. It is based on the concept of Lie groups and Lie algebras, which are mathematical structures that describe the symmetries of a system.…”