Biswas Arshed Model Research Articles

Soliton dynamics and chaotic analysis of the Biswas–Arshed model

Soliton dynamics and chaotic analysis of the Biswas–Arshed model

On nonlinear optical solitons of fractional Biswas-Arshed Model with beta derivative

The Biswas-Arshed (BA) model is an essential wave propagation model in nonlinear optics and optical fibers. In this manuscript, the enhanced G′/G-expansion method is taken into consideration. The BA model is used with this technique to locate visual soliton solutions. The solutions to the hyperbolic and trigonometric functions are determined using this technique. Each solution includes a large number of model and method parameters. The wave solutions are defined by the waves' character, which is determined by the three-dimensional (3D) and two-dimensional (2D) wave patterns with varying parameter values. The structure of the soliton shifts depending on the specific values of the parameters. These shifts are reflected in the 2D pictures that demonstrate the various soliton configurations. Finally, the obtained soliton solutions can be applied to high-speed data transmission to describe propagation pulses and to transmit light between two ends in optical fibers and communication systems.

Soliton Solutions to the BA Model and (3 + 1)‐Dimensional KP Equation Using Advanced exp(−ϕ(ξ))‐Expansion Scheme in Mathematical Physics

In this manuscript, the primary motivation is the implementation of the advanced exp(−ϕ(ξ))‐expansion method to construct the soliton solution, which contains some controlling parameters of two distinct equations via the Biswas–Arshed model and the (3 + 1)‐dimensional Kadomtsev–Petviashvili equation. Here, the solutions’ behaviors are presented graphically under some conditions on those parameters. The height of the wave, wave direction, and angle of the obtained wave is formed by substituting the particular values of the considerations over showing figures with the control plot. With the collaboration of the advanced exp(−ϕ(ξ))‐expansion method, we construct entirely the solitary wave results as well as rogue type soliton, combined singular soliton, kink, singular kink, bright and dark soliton, periodic shape, double periodic shape soliton, etc. Therefore, it is remarkable to perceive that the advanced exp(−ϕ(ξ))‐expansion technique is a simple, viable, and numerical solid apparatus for clarifying careful outcomes to the other nonstraight equivalences.

Bifurcation Analysis and Bounded Optical Soliton Solutions of the Biswas-Arshed Model

We investigate the bounded travelling wave solutions of the Biswas-Arshed model (BAM) including the low group velocity dispersion and excluding the self-phase modulation. We integrate the nonlinear structure of the model to obtain bounded optical solitons which pass through the optical fibers in the non-Kerr media. The bifurcation technique of the dynamical system is used to achieve the parameter bifurcation sets and split the parameter space into various areas which correspond to different phase portraits. All bounded optical solitons and bounded periodic wave solutions are identified and derived conforming to each region of these phase portraits. We also apply the extended sinh-Gordon equation expansion and the generalized Kudryashov integral schemes to obtain additional bounded optical soliton solutions of the BAM nonlinearity. We present more bounded optical shock waves, the bright-dark solitary wave, and optical rogue waves for the structure model via these schemes in different aspects.

Application of the unified method to solve the Biswas–Arshed model

We apply the unified method to retrieve optical soliton solutions of the Biswas–Arshed model (BAM) with the Kerr law nonlinearity in this paper. We first derive the ordinary differential form of this model from its partial differential form via a variable transformation. Then we add many new dynamical solitons of combo trigonometric, hyperbolic, and rational function solutions by Maple-18 package in this literature. The derived solutions exhibit some dynamics as singular solitons with exponentially increasing and decreasing amplitudes, singular solitons with gradually increasing and decreasing amplitudes, and singular solitons with constant amplitudes. Moreover, W-shaped solitons with multiple bright and dark waves, double periodic optical solitons with exponentially increasing and decreasing amplitudes, and double periods with symmetric and asymmetric amplitudes are obtained. Besides this, various dynamical properties of the obtained solutions are presented graphically.

Effect of the free parameters on the Biswas-Arshed model with a unified technique

The solitary dynamics of the Biswas–Arshed (BA) model without self-phase modulation are investigated in the present study. To compensate for the deserted small group velocity dispersion, the BA model includes higher-order spatio-temporal dispersion. The optical soliton solutions of the BA model are examined to use the unified strategy. The solutions to the BA model's nonlinear forms are rogue wave, periodic wave solution, periodic combined singular soliton, combined singular soliton, and periodic wave solution. The three-dimensional (3D) and two-dimensional (2D) graphs depict the dynamical physical appearance of the obtained solutions. We compared our results to those found in the existing studies. The 2D comparison chart additionally explored the consequences of the wave profile based on the values of the parameters k and δ. Finally, this technique can solve increasingly complex models, yielding a large number of soliton solutions.

The dynamical study of Biswas–Arshed equation via modified auxiliary equation method

The presented work deals with the investigation of Biswas–Arshed model which has great importance in the theory of solitons. The proficient approach, namely, modified auxiliary equation (MAE) method is practiced. This method provides results in the form of hyperbolic, trigonometric and rational functions. The dynamical behavior of obtained results is observed through graphs by assigning particular values to free parameters.

New optical soliton solutions of Biswas–Arshed model with Kerr law nonlinearity

In this paper, the newly derived solutions for the optical soliton of Kerr law nonlinearity form of Biswas–Arshed model are investigated. The exact solutions are extracted by deploying two different novel methods namely, [Formula: see text]-expansion method and Riccati–Bernoulli sub-ODE method. Furthermore, in different conditions, the resultants show different wave solutions like singular, kink, anti-kink, periodic, rational, exponential and dark soliton solutions. Also, the dynamics of the attained solutions are presented graphically.

Painlevé analysis of a nonlinear Schrödinger equation discussing dynamics of solitons in optical fiber

In this paper, we investigated a new form of nonlinear Schrödinger equation (NLSE), namely the Biswas–Arshed model (BAM) for the analysis of complete integrability with the help of Painlevé test ([Formula: see text]-test). By applying this test, we analyze the singularity structure of the solutions of BAM, knowing the fact that the absence of specific sort of singularities like moveable branch points is a patent signal for the complete integrability of the discussed model. Passing the [Formula: see text]-test is a powerful indicator that the studied model is resolvable by means of inverse scattering transformation (IST).

On the exact solutions to Biswas–Arshed equation involving truncated M-fractional space-time derivative terms

In this work, two different schemes, the extended hyperbolic auxiliary and the simplest equation method, are employed to construct the exact solutions involving parameters of the Biswas–Arshed model (BAM) with truncated M-fractional derivative. Moreover, semi-inverse variational principle are applied to underlying equation to acquire analytical solution. These methods have a broad applicability to many other nonlinear evolution equations in mathematical physics. Different traveling wave solutions have been investigated by invoking these methods. 3D graphic representations are given to explain the principal effect of parameter μ on dynamical properties of the soliton solutions. The stability property of the obtained solutions is tested to show the ability of our obtained solutions through the physical experiments. Moreover, the general solution of nonlinear ordinary differential equation corresponding to underlying equation is found using traveling wave reduction.

Optical solutions of Biswas–Arshed equation in optical fibers

This paper studies the Biswas–Arshed model that compensates for the group velocity dispersion (GVD) by the dispersion of time and space. When the GVD and non-linearity are very small, the propagation patterns of the model are given by the complete discriminant system for polynomial method. Based on the results, under the specific parameters, we analyze the soliton transmission dynamic.

Chirp-free optical dromions for the presence of higher order spatio-temporal dispersions and absence of self-phase modulation in birefringent fibers

In this paper, we study Biswas–Arshed (BA) model in birefringent fibers for chirp-free solitons (dromions) with the aid of sub-ordinary differential equations (ODE) method. The BA model studies the soliton transmission in optical fiber. We obtain bright, periodic, and Weierstrass elliptic function solutions with constraint conditions.

Optical soliton solutions to Biswas–Arshed model with truncated M-fractional derivative

In this article, the Biswas–Arshed model (BAM) with truncated M-fractional derivative is assumed to secure its different new optical soliton solutions. For this purpose two different schemes, the extended Sinh–Gordon equation expansion (ShGEE) and the modified (G′/G2)-expansion schemes, are applied. As a process, a sequence of traveling wave soliton solutions are obtained and are verified with the help of symbolic soft computations. Obtained soliton solutions, including dark, bright, singular and many others, show that the suggested schemes are effective and reliable as compared to many other schemes. Moreover, the solutions are new as the model of this article is its new form. The main character of the parameter μ on the dynamical features of the obtained optical soliton solutions is also explained with help of three-dimensional graphs.

Optical soliton solutions of the Biswas-Arshed model by the expansion approach

In this paper, we consider the Biswas-Arshed model (BAM) with nonlinear Kerr and power law. We integrate these nonlinear structures of the BAM to obtain optical exact solitons that passing through the optical fibers. To retrieve the solutions, we apply the expansion integral scheme to the structures of the BAM nonlinearity. The novel solutions present optical shock wave, double periodic optical solitons, interaction between optical periodic wave and optical solitons, and optical periodic and rogue waves for both structures of the model. It is shown that the amplitude of the periodic double solitons waves gradually increases and reached the highest peak at the moment of interaction, and it goes to diminish for a much larger time. In fact, we show that the amplitude of the wave for the interaction between periodic and optical solitons, gradually increases with beat phenomena. To the purpose, all these types of optical solitons can be frequently used to amplify or reduce waves for a certain hight. Moreover, we describe the physical phenomena of the solitons in graphically.

Optical solitons to the Biswas–Arshed model in birefringent fibers using couple of integration techniques

This work scrutinizes optical solitons in birefringent fibers with the advocacy of a novel model, the Biswas–Arshed equation with higher order dispersions in Kerr-law media, where four-wave mixing terms are not included. Two resourceful integration techniques which are auxiliary equation method and Sine–Cosine method are utilized to formulate various traveling wave solutions including bright solitons, singular solitons and periodic singular solutions. From the mathematical analysis some constraint relations are observed that guarantee the existence of solitons. Moreover, for the physical understanding of the obtained results, various 3D and 2D graphs are presented.

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.

Optical travelling wave solutions for the Biswas–Arshed model in Kerr and non-Kerr law media

This paper scrutinises the newly proposed Biswas–Arshed model for soliton propagation through optical fibres, with small group velocity dispersion and in the absence of self-phase modulation. Spatio-temporal dispersions of higher order are considered to balance with group velocity dispersion. First integral and functional variable methods are employed to recover solitary wave, shock wave, singular wave and singular periodic wave solutions for the two nonlinear forms of the model through Kerr law and power-law nonlinearity. The constraint relations are also figured for the manifestation of these optical solutions.

Exploring the dark and singular soliton solutions of Biswas–Arshed model with full nonlinear form

In this paper, the optical solitons of two nonlinear forms, namely Kerr type and power law form, of Biswas–Arshed model are studied. To construct optical solitary wave solutions of the aforementioned model, the modified extended tanh expansion method was used successful. As a consequence, many new optical solitons including, dark, singular, dark/singular, and periodic soliton solutions are retrieved and verified through MATHEMATICA.

Optical solitons in birefringent fibers with Biswas–Arshed model by generalized Jacobi elliptic function expansion method

In this paper, we employ a generalized Jacobi elliptic function expansion method to extract optical solitons and other solutions to Biswas–Arshed model in birefringent fibers. Jacobi elliptic functions solutions, bright solitons, singular solitons, dark solitons, periodic wave solutions and other solutions have been found.

Optical singular and dark solitons with Biswas–Arshed model by modified simple equation method

This paper investigates the soliton dynamics of Biswas–Arshed model in the absence of self-phase modulation. This model contains higher order spatio-temporal dispersion in compensation with negligibly small group velocity dispersion. A dynamic integration scheme, modified simple equation method, is utilized in order to recover singular and dark soliton solutions to the two nonlinear forms of this model through Kerr law and power law of nonlinearity. Whereas a rational solution is also obtained as a by-product. Moreover, the dynamical characteristics of the obtained solutions are presented by 3D and 2D plots. Various constraint relations are also listed which ensures the existence of solitons.