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The principal purpose of this research is to utilize the exp-function approach for achieving exact solutions of nonlinear optical fibers, including fractional order in the sense of conformable derivatives. Owing to the algorithm of symbolic computational, Some soliton solutions are obtained, including solitary soliton, singular kink-type soliton, and periodic solitons. These results are generated and developed by using the exp-function. To the greatest of our knowledge, the soliton solutions given in this study could be highly beneficial in comprehending physical phenomena. [ABSTRACT FROM AUTHOR]

In this work, we investigate diverse analytical solutions and modulation instability of the nonlinear Schrödinger equation with an anti-cubic nonlinear term. We use the traveling wave transformation and the New Generalized Extended Direct Algebraic Method to perform a variety of exact traveling wave soliton-like solutions. The obtained solutions are among other trigonometric function solutions, complex soliton solutions, and rational solutions. A particular behavior has been depicted in self-focusing and defocusing nonlinearity where dark soliton changes to super rogue waves and breather soliton is obtained. We then use the linearizing scheme to get the growth rate of modulation instability. For a specific value of the excitation wave number and a specific time of simulation, diverse waveforms of the modulated waves are obtained. We have demonstrated that the combined dispersion and nonlinear terms, as well as the anti-cubic nonlinear term, can develop modulation instability. To confirm the predictions based on the analytical results, we use the direct numerical simulation, from which we have displayed a modulation wave of the growth rate modulation instability. It results equally that the anti-cubic nonlinearity is an important object to control the propagation of the solitonic waves in the nonlinear systems. [ABSTRACT FROM AUTHOR]

The propagation of optical solitons via nonlinear metamaterials with cubic-quintic nonlinearity, detuning intermodal dispersion, self steepening effect, and nonlinear third and fourth-order dispersions is the focus of this study. To find the optical solitons and other solutions, the extended sinh-Gordon equation expansion method is applied to the aforementioned model. As a result, dark, bright, combined dark–bright, singular, combined singular soliton, and singular periodic wave solutions are obtained. To our best knowledge, the application of the method to the model, and the acquired combined soliton solutions are novel. To understand the nonlinear propagation theory of solitons in metamaterials, the reported outcomes can be enriched by the soliton theory. [ABSTRACT FROM AUTHOR]

In this paper, we implemented extended e x p - φ ξ -expansion method for some exact solutions of (3 + 1)-dimensional nonlinear Schrödinger equation (NLSE) and coupled nonlinear Schrodinger's equation. The solutions we obtained are hyperbolic, trigonometric and exponential solutions. We observed that these solutions provided the equations through Mathematica 11.2. Apart from that, we have shown the graphics performance of some of the solutions found. This method has been used recently to obtain exact traveling wave solutions of nonlinear partial differential equations. The results achieved in this study have been confirmed with computational software Maple or Mathematica by placing them back into NLFPDEs and found them correct. We posited that the approach is updated to be more pragmatic, efficacious, and credible and that we pursue more generalized precise solutions for traveling waves, like the solitary wave solutions. [ABSTRACT FROM AUTHOR]

We are concerned with new form optical solitons to the non-linear Schrödinger equation (NLSE) by generalized anti-cubic non-linearity. Some new optical solitons containing dark, singular and periodic solitons in chirp-free and chirped form are constructed via modified extended tanh expansion method. These results are very useful in the field of optics. The obtained results are verified and also explain by drawing different graphs. Parametric conditions for the chirp-free and chirped shape soliton solutions are also mentioned. Computational results indicate the efficiency of the aforesaid analytical expansion scheme. [ABSTRACT FROM AUTHOR]

In this paper, we considered the nonlinear Schrodinger equation modeling cubic optical solitons in a polarization-preserving fiber with Kerr law. Using the improved t a n (φ / 2) -expansion method, a powerful and effective method, we constructed exact solutions including the hyperbolic function solution, the trigonometric function solution, the exponential solution and the rational solution with free parameters. The geometrical shapes for some of the obtained results are depicted for various choices of the free parameters that appear in the results. The obtained solutions are entirely new and can be considered as generalization of the existing results in the ordinary derivative case. [ABSTRACT FROM AUTHOR]

This article is concerned with analyzing exact optical soliton solutions to Kudryashov's model. To this end, the sine-Gordon expansion and Kudryashov methods are exerted and a bunch of new optical soliton solutions is acquired. The implementation and algebraic methods are discussed in detail. Finally, singular and bright-dark soliton solutions emerge from the scheme and the existing criteria for such solutions are elucidated. [ABSTRACT FROM AUTHOR]

In this paper, the perturbed nonlinear Schrödinger equation with dual-power law of nonlinearity is studied by adopting four mathematical methods namely the Modified Kudryashov method, the extended Tanh–Coth method, the modified simple equation method and soliton ansatz method. As a results, a set of various types of solitons that contains dark, singular, dark–singular, bright optical solitons and other form of optical soliton solutions are obtained. Firstly, we solve the perturbed nonlinear Schrödinger equation by considering the dual power law parameter using the first three integration methods and secondly we set this parameter equal to one in order, to solve the problem with the fourth method. The used methods in this paper present various applications in fields of nonlinear wave equations. Comparing our new results with well-known in literature are also given. Moreover, the graphical representations of the modulus of some optical soliton solutions and their 2-D profile are also depicted. [ABSTRACT FROM AUTHOR]

Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Correction to: Optical solitons of (3 + 1) dimensional and coupled nonlinear Schrodinger equations Correction to: https://doi.org/10.1007/s11082-022-03613-yhttps://doi.org/10.1007/s11082-022-0... The article with title "Optical solitons of (3 + 1) dimensional and coupled nonlinear Schrodinger equations" has been published twice with https://doi.org/10.1007/s11082-022-03613-y and https://doi.org/10.1007/s11082-022-03599-7. [Extracted from the article]