Browsing by Author "Raza N."

Now showing 1 - 13 of 13

A new exploration of some explicit soliton solutions of q-deformed Sinh-Gordon equation utilizing two novel techniques
(2023-03-01) Raza N.; Butt A.R.; Arshed S.; Kaplan M.
In the present work, the q-deformed Sinh-Gordon equation considered by performing new extended generalized Kudryashov method and improved tan(Φ2)-expansion method. Thanks to these methods, we can effectively obtain rational, hyperbolic and trigonometric solutions by specially choosing the parameters for the existence of solutions. The proposed equation expands the possibilities for modeling physical systems in which symmetry is broken. The obtained solutions are graphically illustrated.
Abundant soliton-type solutions to the new generalized KdV equation via auto-Bäcklund transformations and extended transformed rational function technique
(2022-08-01) Jannat N.; Kaplan M.; Raza N.
This study investigates new soliton-type solutions to the new generalized KdV (ngKdv) equation. For this purpose, the homogeneous balance method is used to create Auto-Bäcklund transformations of the regarded equation and with the help of the transformations, abundant exact and explicit solutions have been found. We found complexiton solutions to the dealt equation by using the extended transformed rational function technique. We have also given the 3D graphics of the obtained solutions.
An effective computational approach and sensitivity analysis to pseudo-parabolic-type equations
(2021-01-01) Kaplan M.; Butt A.R.; Thabet H.; Akbulut A.; Raza N.; Kumar D.
The researchers have developed numerous analytical and numerical techniques for solving fractional partial differential equations most of which provide approximate solutions. Exact solutions, however, are vitally important in a convenient conception of the qualitative properties of the concerned phenomena and processes. In this paper, the pseudo-parabolic-type equations with conformable fractional derivatives are reduced to conformable fractional nonlinear ordinary differential equations by implementing a simple wave transformation. An important benefit of the proposed transformation is that it yields analytical solutions of the conformable pseudo-parabolic type equations by applying the exponential rational function strategy. The sensitivity behaviour of the model has been mentioned thoroughly.
An exploration of novel soliton solutions for propagation of pulses in an optical fiber
(2022-07-01) Raza N.; Arshed S.; Kaplan M.; Butt A.R.
In this article, the propagation of pulses in optical fiber has been studied by considering the nonlinear partial differential equation (NPDE). The proposed model is investigated using two analytical techniques namely the Sine-Gordon expansion (SGE) procedure and the modified auxiliary equation (MAE) method. The trigonometric function, hyperbolic function, and rational function solutions have been extracted from the proposed methods. The employed procedures are compatible in obtaining traveling wave solutions. Moreover, the obtained results are assisted with 3D graphs to demonstrate the physical significance and dynamical behaviors by using different parameter values.
Complexiton and resonant multi-solitons of a (4 + 1)-dimensional Boiti–Leon–Manna–Pempinelli equation
(2022-02-01) Raza N.; Kaplan M.; Javid A.; Inc M.
This work is concerned with the extraction of auto-Bäcklund transformations of (4 + 1)-dimensional Boiti–Leon–Manna–Pempinelli (BLMP) equation in accordance with the extended homogeneous balance (HB) method incorporating Maple. Subsequently, these transformations are used to study analytic explicit solutions of this equation. Also, based on the Hirota bilinear form and the extended transformed rational function method, complexiton solutions have been found of the (4 + 1)-dimensional BLMP equation through a direct symbolic computation with Maple. This method is the improved form of the transformed rational function method. The obtained complexiton solutions, including trigonometric and hyperbolic trigonometric solutions, have been verified utilizing Hirota bilinear forms. Some of the solutions are depicted in 3D graphs to understand physical properties. The reported results are new and have applications in several scientific fields such as incompressible fluids.
Construction of complexiton-type solutions using bilinear form of Hirota-type
(2023-02-01) Kaplan M.; Raza N.
In this paper, based on the Hirota bilinear form and the extended transformed rational function method, complexiton solutions have been found of the Hirota-Satsuma-Ito (HSI) equation and generalized Calogero-Bogoyavlenskii-Schiff equation through a direct symbolic computation with Maple. This method is the improved form of the transformed rational function method. The obtained complexiton solutions, includes trigonometric and hyperbolic trigonometric solutions, have verified utilizing Hirota bilinear forms. Also, a graphical representation of the obtained solutions is given.
Dynamics of Lump, Breather, Two-Waves and Other Interaction Solutions of (2+1)-Dimensional KdV Equation
(Springer, 2023) Jannat N.; Raza N.; Kaplan M.; Akbulut A.
In this investigation, we address a particular variant of the Korteweg–de Vries (KdV) equation, specifically focusing on the (2+1)-dimensional KdV equation. The equation can model various physical phenomena in different fields, including fluid dynamics, plasma physics, nonlinear optics, and other areas where coupled wave interactions are important. To commence, we establish the Auto-Bäcklund and Cole–Hopf transformations for the given model, resulting in the derivation of numerous soliton-like solutions characterized by hyperbolic, trigonometric, and exponential function waves. Furthermore, we effectively elucidate the behavior of lump, lump–kink, breather, two-wave, and three-wave solutions using the Hirota bilinear technique. Extensive numerical simulations employing 3-D profiles are conducted with meticulous consideration of pertinent parameter values, providing additional insights into the distinctive traits of the obtained solutions. Moreover, employing the extended transformed rational function method grounded in the bilinear form of the underlying equation, we uncover complexiton solutions. These solutions are depicted using 3-D and 2-D visualizations to portray their dynamics. Our findings reveal that the approach adopted to derive analytical solutions for nonlinear partial differential equations proves to be both efficient and potent. The combination of numerical simulations and visual representations enhances our understanding of these solutions, ultimately affirming the effectiveness and robustness of the employed methodology in tackling nonlinear partial differential equations.
Exact periodic and explicit solutions of higher dimensional equations with fractional temporal evolution
(2018-03-01) Raza N.; Sial S.; Kaplan M.
The term soliton has been used for a pulse like nonlinear wave (solitary wave) which leaves an interaction with unaltered shape and speed. To date, no less than seven particular wave frameworks or systems have been found to show such solutions. This speaks to an extensive variety of utilizations in applied science. The Exp(−ϕ(ξ))-expansion technique is utilized to find generalized solitary solutions and intermittent or periodic solutions for nonlinear evolution equations emerging in mathematical physics with the use of the enhanced time conformable equation. The technique is direct and succinct, and its applications are promising for other nonlinear mathematical physics.
Optical soliton solutions of the cubic-quintic non-linear Schrödinger’s equation including an anti-cubic term
(2018-07-12) Kaplan M.; Hosseini K.; Samadani F.; Raza N.
A wide range of problems in different fields of the applied sciences especially non-linear optics is described by non-linear Schrödinger’s equations (NLSEs). In the present paper, a specific type of NLSEs known as the cubic-quintic non-linear Schrödinger’s equation including an anti-cubic term has been studied. The generalized Kudryashov method along with symbolic computation package has been exerted to carry out this objective. As a consequence, a series of optical soliton solutions have formally been retrieved. It is corroborated that the generalized form of Kudryashov method is a direct, effectual, and reliable technique to deal with various types of non-linear Schrödinger’s equations.
Painlevé analysis, dark and singular structures for pseudo-parabolic type equations
(2022-08-10) Arshed S.; Raza N.; Kaplan M.
In this paper, two important pseudo-parabolic type equations are studied for extracting soliton solutions via the generalized projective riccati equations method. These equations are Oskolkov equation and Oskolkov-Benjamin-Bona-Mahony-Burgers equation. The proposed method extracts dark soliton and singular soliton. Furthermore, the Painlevé test (P-test) has also been employed on pseudo-parabolic type equations for investigating integrability. The proposed equations are proved to be integrable by P-test. The numerical simulations have also been carried out by 3D and 2D graphs of some of the obtained solutions.
Research on sensitivity analysis and traveling wave solutions of the (4 + 1)-dimensional nonlinear Fokas equation via three different techniques
(2022-01-01) Kaplan M.; Akbulut A.; Raza N.
In the current manuscript, (4 + 1) dimensional Fokas nonlinear equation is considered to obtain traveling wave solutions. Three renowned analytical techniques, namely the generalized Kudryashov method (GKM), the modified extended tanh technique, exponential rational function method (ERFM) are applied to analyze the considered model. Distinct structures of solutions are successfully obtained. The graphical representation of the acquired results is displayed to demonstrate the behavior of dynamics of the nonlinear Fokas equation. Finally, the proposed equation is subjected to a sensitivity analysis.
Symbolic computation and sensitivity analysis of nonlinear Kudryashov's dynamical equation with applications
(2021-10-01) Raza N.; Seadawy A.R.; Kaplan M.; Butt A.R.
This article aims to identify solitary wave solutions to a nonlinear Kudryashov's equation utilizing an exponential rational function method and Painlevé approach. This model is used to interpret the propagation of modulated envelope signals which disseminate with some group velocity. These two different methods are applied to build analytical solutions of the model that are relatively new and effective to solve the nonlinear evolution equation. Hyperbolic wave function and kink solitons are two types of traveling wave solutions that can be obtained using these techniques. For the existence of these solitons, constraint conditions on the parameters have also been listed. Graphical illustrations have also been given to understand the physical significance of the proposed model. In the end stability analysis of the obtained solution is carried out for depicting the importance of the model.
The unified method for abundant soliton solutions of local time fractional nonlinear evolution equations
(2021-03-01) Raza N.; Rafiq M.H.; Kaplan M.; Kumar S.; Chu Y.M.
This work studies two important temporal fractional nonlinear evolution equations, namely the (2+1)-dimensional Chaffee–Infante equation and (1+1)-dimensional Zakharov equation by way of the unified method along with properties of local M-derivative. The typical structures of fractional optical soliton wave solutions are obtained in polynomial and rational forms. Further, to grant the validity of non-singular solutions are given with limitation conditions and graphically depicted in 3D. Also, to expose the effect of a local fractional parameter on expected non-singular solutions are depicted through 2D graphs. The predicted solutions are revealing that the proposed approach is straightforward and valuable to find the solitary wave solutions of other nonlinear evolution equations.