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In this paper, we find new solitons solutions of the complex Ginzburg-Landau equation with Kerr law nonlinearity according to the new extended direct algebraic method. When parameters involving this method are taken to be special values we can obtain the solitary wave solutions which is derived from other methods such as, the ( G ′/ G )–expansion method, the modified Kudryashov method, the extended tanh-function method and so on. It is shown that the new extended direct algebraic method, with the help of symbolic computation, provides a more powerful mathematical tool for many other solving nonlinear partial differential equations. [ABSTRACT FROM AUTHOR]

The soliton dynamics in optical fibers with Fokas–Lenells equation is illustrated in this paper. Bright, dark and singular soliton solutions are retrieved along with few forms of combo-soliton solutions that also naturally emerged from the three integration schemes applied to the model. The existence criteria of these solitons are also presented. [ABSTRACT FROM AUTHOR]

This paper studies fractional temporal evolution of optical solitons with quadratic–cubic nonlinearity that comes with a few perturbation terms. Khalil's conformable fractional derivative as well as Liu's extended trial function scheme are applied to retrieve these soliton solutions. The results are applicable to mitigate Internet bottleneck that is a growing problem in telecommunications industry. [ABSTRACT FROM AUTHOR]

In recent years, finding exact solutions to nonlinear differential equations has become a fascinating study topic. In the present study, using the modified Kudryashov method and the improved generalized Riccati equation mapping method in the conformable sense, we acquired the exact soliton-type solutions for the new time-fractional perturbed Boussinesq-like equation. This equation has been successfully obtained by the use of asymptotic methods on the defocusing Camassa–Holm nonlinear Schrödinger equation. We obtain the exponential, trigonometric, hyperbolic, and rational type solutions comprising dark solitons, kink solitons, bisymmetry solitons, singular solitons, combined complex solitons, and periodic solutions. These solutions are of great importance in various fields of applied sciences, coastal, and ocean engineering. Furthermore, all acquired solutions have been validated by putting them back into the original equation with the help of the Mathematica package software. • The conformable Boussinesq-like equation is considered. • The modified Kudryashov and the improved generalized Riccati equation mapping methods are used. • The obtained solutions are given by 2D and 3D figures. • The exponential, trigonometric, hyperbolic, rational type, combined complex solitons, and periodic solutions are acquired for the model problem. [ABSTRACT FROM AUTHOR]

This paper secures dark and singular resonant optical solitons that is studied with dual-power law nonlinearity and fractional temporal evolution. Khalil's conformable fractional derivative is put into perspective to retrieve these soliton solutions. The parameter restrictions for the existence of such solitons are also indicated. [ABSTRACT FROM AUTHOR]

Presented herein is an exact examination on the resonant nonlinear Schrödinger equation (RNLSE) with Kerr law nonlinearity considering inter-modal dispersion and spatio-temporal. To this end, the ordinary differential equation (ODE) is derived from the traveling wave transformation. Then, the new extended direct algebraic method (NEDAM) is utilized in the axial direction to obtain the results of this study. Subsequently, a bunch of optical soliton solutions in conjunction with dark, bright, and dark-bright soliton solutions are plotted. As a result, it is verified the methodology has an effective mathematical gadget to solve nonlinear partial differential equations (NPDEs). [ABSTRACT FROM AUTHOR]

This study reveals the dark, bright, combined dark–bright, singular optical solitons and other solutions to the conformable space–time fractional Fokas–Lenells equation. We use two integral schemes in reaching such solutions. The constraints conditions which guarantee the existence of valid solutions are stated. By choosing the suitable values of the parameters involved, we plot the 2-dimensional and 3-dimensional surfaces to some of the obtained solutions. [ABSTRACT FROM AUTHOR]

Stochastic equations are powerful mathematical tools used to study systems having random effects. The current manuscript studies the two distinct systems: the stochastic conformable Zakharov system (SCZs) and stochastic conformable Hirota-Macari system (SCHMs) with multiplicative noises. Both systems are investigated using the conformable derivative in terms of stratonovich formulation. These systems are chosen for study due to their relevance and significance in understanding the behavior of complex physical phenomena influenced by stochastic effect. The novelty lies in the applications of the unified solver method, which is a succinct, direct and efficient technique for obtaining solutions in rational, trigonometric and hyperbolic forms. To demonstrate the effect of multiplicative noise and conformable derivative on the solutions of SCZs and SCHMs, 3D and 2D graphs are illustrated by using Mathematica 11. Our findings highlight the sustaining role of the multiplicative noise, which stabilizes the solutions of systems around zero. Overall, this study deepens the understanding of the interaction between stochastic effects and conformable derivatives in the context of these complex systems. • The unified solver method is used to solve the stochastic conformable Zakharov system. • Innovative rational, trigonometry and hyperbolic stochastic solutions are given for the model problem. • The dynamical features of obtained results are demonstrated through interesting plots. [ABSTRACT FROM AUTHOR]