Combo Solitons Research Articles

On some novel solitons to the generalized (1 + 1)-dimensional unstable space–time fractional nonlinear Schrödinger model emerging in the optical fibers

In this study, a state-of-the-art approach tilted as the extended modified auxiliary equation mapping method is employed to observe some novel exact solutions to the generalized (1 + 1)-dimensional unstable space–time fractional nonlinear Schrodinger model. A variety of solitons are discovered namely, bright, dark, singular, combo, optical, singular optical and combo solitons in an elegant scheme. The existence conditions are also presented by choosing appropriate parameters to visualize the physical interpretation of solitons in three-dimensions with the aid of the latest computational tools.

Solitons and conservation laws in magneto-optic waveguides with polynomial law nonlinearity

Two prolific integration algorithms, extended Kudryashov's method and generalized Jacobi's elliptic function expansion, led to optical soliton solutions to magneto-optic waveguides maintaining polynomial law of nonlinear refractive index. Bright, singular and combo soliton solutions have thus emerged. A couple of solutions in terms of Weierstrass’ elliptic functions are also presented. Finally, the corresponding conservation laws are enumerated.

Optical Solitons of Biswas-Arshed Model in Birefrigent Fiber Without Four Wave Mixing

In this paper, we apply the undetermined coefficient method and modified mapping method to extract the bright, dark, singular, periodic singular, dark-singular combo solitons of Biswas-Arshed equation (BAE) in birefringent fibers. Many new exact solutions are acquired by proposed techniques. The computation effort and constructed exact solutions validate the effectiveness, easiness, and impact of the current techniques.

Soliton solutions of higher-order nonlinear schrödinger equation (NLSE) and nonlinear kudryashov's equation

This article secures new soliton solutions of the higher-order nonlinear Schrödinger equation (NLSE) and the nonlinear Kudryashov's equation by means of two analytical techniques, namely the extended (G′G2)-expansion method and the first integral method. Many exact traveling wave solutions such as hyperbolic function solutions, trigonometric function solutions and rational function solutions with free parameters are characterized. Periodic solitons, dark solitons, singular solitons, combo solitons and plane waves are obtained. The existence criteria for such solutions are also provided. Moreover, the modulation instability analysis is used to examine the stabilities of both equations, by which the modulation instability gain spectrums of both equations are obtained. The obtained solutions are also presented graphically.

Propagation of traveling wave solutions for nonlinear evolution equation through the implementation of the extended modified direct algebraic method

In this work, different kinds of traveling wave solutions and uncategorized soliton wave solutions are obtained in a three dimensional (3-D) nonlinear evolution equations (NEEs) through the implementation of the modified extended direct algebraic method. Bright-singular and dark-singular combo solitons, Jacobi’s elliptic functions, Weierstrass elliptic functions, constant wave solutions and so on are attained beside their existing conditions. Physical interpretation of the solutions to the 3-D modified KdV-Zakharov-Kuznetsov equation are also given.

Propagation of nonlinear waves with a weak dispersion via coupled $$(2+1)$$-dimensional Konopelchenko–Dubrovsky dynamical equation

This work applies the modified extended direct algebraic method to construct some novel exact travelling wave solutions for the coupled $$(2+1)$$ -dimensional Konopelchenko–Dubrovsky (KD) equation. Soliton, periodic, solitary wave, Jacobi elliptic function, new elliptic, Weierstrass elliptic function solutions and so on are obtained, which have several implementations in the field of applied sciences and engineering. In addition, we discuss the dynamics of some solutions like periodic, soliton and dark-singular combo soliton by their evolutionary shapes.

Optical solitons with complex Ginzburg-Landau equation having a plethora of nonlinear forms with a couple of improved integration norms

This paper secures optical soliton solutions from complex Ginzburg-Landau equation that is studied with nine different nonlinear forms. Two types of integration architecture are employed and these are improved versions of their earlier kinds. Bright, dark, singular as well as combo soliton solutions are recovered. Their existence is guaranteed with parameter constraints that are also enumerated.

New optical solitons of Biswas-Arshed equation using different techniques

This paper scrutinizes the newly proposed Biswas-Arshed equation with Kerr and power law nonlinearities for soliton propagation through optical fibers, with small group velocity dispersion and in absence of self-phase modulation. Spatio-temporal dispersions of higher order are considered in compensation with group velocity dispersion. In this work, bright, dark, singular and bright-singular combo soliton solutions are retrieved using undetermined coefficients and Kudryashov's methods.

Optical solitons perturbation of Fokas-Lenells equation with full nonlinearity and dual dispersion

This paper retrieves dark, rational, periodic and combo soliton solutions that stem from Fokas-Lenells equation which is studied with full nonlinearity. These solitons appear with constraint conditions on their parameters and they are also presented. Two strategic schemes have made this retrieval successful.

Optical soliton solutions for nonlinear Schrödinger equation

This piece of research is devoted to study nonlinear Schrödinger equation (NLSE) along with perturbation terms and its soliton solutions. The model is integrated via G′G2-expansion approach and the first integral method. Dark, singular and periodic soliton solutions are retrieved along with kink and anti-kink type soliton solutions that emerged from the two integration schemes applied to the model. Many forms of combo soliton solutions are also listed as a byproduct. The restrictions on the parameters for the existence of these solitons are also presented.

Generalized optical soliton solutions to the (3+1)-dimensional resonant nonlinear Schrödinger equation with Kerr and parabolic law nonlinearities

The resonant nonlinear Schrodinger equation in three dimensions featuring both the Kerr and parabolic law nonlinearities has been considered in this paper due to its vital role in the propagation of solitons in optical fibers. Optical soliton solutions to this important model consisting of dark, singular and combo solitons alongside various periodic solutions that are new and more general to the lately devised solutions have been presented. We also reported the constraint conditions that guarantee the survival of these solitons and depicted certain results.

Optical solitons in birefringent fibers having anti-cubic nonlinearity with exp-function

This paper studies optical solitons in birefringent fibers with anti-cubic nonlinearity. The exp-function scheme retrieves singular and combo solitons. The existence criteria for these solitons are also presented.

Highly dispersive optical solitons in absence of self-phase modulation by exp-function

This paper studies highly dispersive optical solitons when self-phase modulation term is completely absent. The delicate balance for existence and sustaining of solitons is provided by self-steepening effect and nonlinear dispersions. The exp-function approach yields singular and bright-singular combo solitons.

Highly dispersive optical solitons with quadratic–cubic law by exp-function

This paper studies highly dispersive optical solitons by the application of exponential function. The model is with quadratic–cubic nonlinear fibers. The algorithm reveals singular and bright–singular combo soliton solutions. The integrability criteria are also listed in this work.

Optical soliton solutions of the time-fractional perturbed Fokas-Lenells equation: Riemann-Liouville fractional derivative

Based on the Riemann-Liouville fractional derivative, the time-fractional nonlinear Fokas-Lenells equation is analyzed in this paper. The extended simplest equation method is implemented to construct several kinds of solitons such as singular and combo soliton solutions of the present model. The existence criteria of the obtained soliton solutions are also reported. Moreover, it has been shown that the results in the literature are special cases of the present ones when the fractional-order of differentiation becomes unity.

Some analytical solutions by mapping methods for non-linear conformable time-fractional PHI-4 equation

In this paper, the practice of two types of mapping methods are used to solve the time fractional Phi-4 equation by means of conformable fractional derivative. The solutions are derived using Jacobi?s elliptic functions for two different value of the modulus and are obtained the some soliton solutions. The found solutions are iden?tified bright optical soliton, dark soliton, singular soliton, combo soliton solution, and periodic solutions.

Dispersive solitons in optical metamaterials having parabolic form of nonlinearity

This paper studies solitons in highly dispersive optical metamaterials with cubic–quintic nonlinearity in presence of detuning, inter-moda dispersion, self-steepening and nonlinear dispersion. Three forms of integration scheme retrieved solitons and other solutions to the model that included snoidal and snoidal waves. These algorithms retrieved bright, dark, singular as well as dark-singular combo solitons along with their respective existence criteria.

Optical solitons in birefringent fibers with Kundu-Eckhaus equation

This paper employs two strategic integration algorithms to extract soliton solutions to Kundu-Eckhaus equation in the context of birefringent fibers. The two schemes are G′/G2-expansion approach and sine-cosine method. Bright, singular and dark-singular combo solitons are retrieved. With reversed constraint conditions, singular-periodic solutions also emerge, although they are not applicable to the photonics field.

Optical soliton perturbation for Gerdjikov–Ivanov equation via two analytical techniques

This paper employs two integration procedures to obtain soliton solutions to the perturbed Gerdjikov–Ivanov equation. They are G′/G2–expansion method and the sine–cosine method. Bright, dark and singular solitons are revealed along with a few of the combo–soliton solutions. The existence criteria of these solitons are also given.

Optical soliton perturbation of Fokas–Lenells equation with two integration schemes

This paper obtained singular and dark-singular combo solitons to Fokas–Lenells equation by the aid of traveling wave hypothesis. The modified simple equation scheme retrieved plane wave solutions to the model. The existence criteria of these waves are also presented.