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This article deals with the applications of (1 / G ′) -expansion method which has recently been presented to the literature. Applying this tool on the generalized (2 + 1)-dimensional Hirota–Maccari system, perturbed nonlinear Schrödinger's equation and dispersive cubic-quintic nonlinear Schrödinger equation, new complex traveling wave solutions are founded. The solution of partial differential equations representing the phenomenon of fiber optic communication and the interrelationship of the internal dynamics of traveling wave solutions, which play an important role in the transport of energy, have been discussed. Furthermore, for a better physical understanding of the results, various graphs with the appropriate values of the parameters have been presented and the simulation has been used to support the discussion. [ABSTRACT FROM AUTHOR]

In this paper, perturbed Chen–Lee–Liu equation is considered to describe pulse propagation in optical fibers. Chen–Lee–Liu equation is a derivative form of the nonlinear Schrödinger equation. Two renowned analytical techniques namely, exp (- φ (η)) -expansion method and the generalized Kudryashov method are applied to analyze this model. The algorithm of these methods is also presented. Different structures of soliton solutions are successfully investigated for perturbed this model. Additionally, constraint conditions on coefficients of perturbation terms are also defined to assure the existence of such solitons. The graphical representation of these solutions is shown to demonstrate the dynamics of pulse propagation governed by Chen–Lee–Liu equation in optical fibers. [ABSTRACT FROM AUTHOR]

The main goal of this paper is to study the higher-order dispersive extended nonlinear Schrödinger equation, which demonstrates the propagation of ultrashort pulses in optical communication networks. In this study, both the sinh-Gordon expansion method and the generalized exponential rational function method are used to offer some novel optical solutions. These optical soliton solutions are dark soliton, bright soliton, singular, periodic, and dark-bright soliton solutions. The obtained optical soliton solutions are presented graphically in 2D and 3D to clarify the behavior of solutions more effectively. The constraint conditions are also used to verify the exitances of the new analytical solutions. Moreover, all solutions compared to solutions obtained previously are new, and all the new wave solutions have verified Eq. (1) after we substituted them into the studied equation. In the future, these novel soliton solutions will be very helpful in developing fluid dynamics, biomedical issues, dynamics of adiabatic parameters, industrial research, and many other areas of science. To our acknowledgment, the presented optical solutions are novel, and also beforehand these methods have not been applied to this studied equation. [ABSTRACT FROM AUTHOR]

This paper presents an improved Cham method as an efficient technique for obtaining analytical exact solutions to nonlinear partial differential equations. We apply this method to solve the nonlinear Schrödinger equation in conformable operator, a challenging equation frequently used in various scientific fields. The method enables us to derive different traveling wave solutions, such as kink, coindal waves, breather waves, periodic singular solutions, and periodic multi-wave solitons. We also provide graphical representations of some of the obtained solutions to help understand their dynamic characteristics. These results highlight the effectiveness and adaptability of the method and demonstrate its potential to solve other partial differential equations. [ABSTRACT FROM AUTHOR]

This paper deals with a nonlinear Schrödinger equation in the sense of conformable derivative. Bifurcations and phase portraits are first proposed by using bifurcation theory, which investigates the dynamical behavior of this equation. This bifurcation theory classifies the plausible solutions to infinite periodic wave solutions, periodic wave solutions, two kink (anti-kink) wave solutions, and two families of breaking wave solutions. A generalized double auxiliary equation approach that generates three families of exact exact traveling wave solutions is then proposed using the conformable operator under various parameter conditions. The 3D behavior of various solutions with absolute real and imaginary parts is displayed. The obtained results show that the proposed methodology is efficient and applicable to a broad class of conformable nonlinear partial differential equations in mathematical physics. [ABSTRACT FROM AUTHOR]

This paper concerns with the integrability of variable coefficient fifth order nonlinear Schrödinger's equation describing the dynamics of attosecond pulses in inhomogeneous fibers. Variable coefficients incorporate varying dispersion and nonlinearity which are of physical significance in considering the nonuniform boundaries of fibers as well as the inhomogeneities of the media. The well-known exp(−φ(s))-expansion method is used to retrieve singular and periodic solitons with the aid of symbolic computation. The structures of the obtained solutions are discussed along with their existence criteria. Moreover, the modulation instability analysis is carried out to identify the instability regions. A dispersion relation is extracted between wave number and frequency. The optimal value of the frequency is found for the occurrence of the instability. A detailed discussion of the results is also given along with graphics. [ABSTRACT FROM AUTHOR]

This paper studies (2 + 1) -dimensional stochastic chiral nonlinear Schrödinger equation dynamically. A number of novel solutions such as periodic, singular, dark and bright solitons solutions are retrieved. The extraction of these solutions is helped by three efficient and robust integration tools such as the Kudryashov's R function method, Jacobi elliptic function method (JEFM) and the modified auxiliary equations (MAE) method. The parametric constraints for the existence of such solutions are also listed. Moreover, 3D plots of few obtained solutions are presented in this paper. [ABSTRACT FROM AUTHOR]