The analysis of exact solitons solutions in monomode optical fibers to the generalized nonlinear Schrödinger system by the compatible techniques

Abstract

In this research work, we employ the unified method, the extended sinh-Gordon equation expansion method (ShGEEM), and the extended rational sine-cosine/sinh-cosh method to derive the novel optical solitons solutions of the (2+1)-dimensional nonlinear dynamical conformable fractional generalized Schrödinger system in monomode optical fibers. We extract the optical soliton solutions in diverse forms like, dark, bright, combinations of dark-bright, periodic, and singular solutions, that are presented by trigonometric functions, and hyperbolic functions. The employed procedures are useful for clarifying nonlinear partial differential equations (NLPDEs) and secure new exact solutions in addition to previously recovered ones. The accuracy of these answers has been verified for all extracted results using the Mathematica. The 3D surface plots, 2D line plots, and associated contour graphs are used to analyze the obtained solutions to visualize and support the theoretical conclusions using appropriate parameter values. The findings of this research demonstrate the efficacy of the approaches taken in enhancing nonlinear dynamical behavior.

Optical soliton solutions of fokas system and (2 + 1) Davey-Stewartson system by mapping method

“…Singular solitons are waves with discontinuous derivatives and have importance in the study of rogue waves. Authors in [32] studied conformable model in different Cartesian plane by using three different methods to derive the novel optical solitons solutions, our results are unique and different, moreover, by analyzing our results with some other lately derived solutions in [23][24][25]27], we witness that our solutions are exclusive and the latest and haven't been reported in literature previously. This work might help researchers to understand the physical properties of these models, especially in the field of nonlinear optics, water waves phenomena.…”

New soliton solutions of kraenkel-manna-merle system with beta time derivative

“…Nonlinear evolution equations (NLEEs) have important applications in mathematical chemistry, mathematical physics, hydrodynamics, biophysics, geochemistry, control theory, mechanics, meteorology, chemical kinematics, optics, biogenetics and many other fields of science. Many researchers have presented various solution methods to obtain the solutions of NLEEs [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20].…”