Browsing by Author "Kaabar M.K.A."

Now showing 1 - 14 of 14

A new computational approach to the fractional-order Liouville equation arising from mechanics of water waves and meteorological forecasts
(2022-01-01) Yue X.G.; Zhang Z.; Akbulut A.; Kaabar M.K.A.; Kaplan M.
The current analysis employs the improved F-expansion, modified extended tanh, exponential rational function, and (g′)−expansion procedures to find a divergent collection of the fractional Liouville equation's exact solutions in the context of beta-derivative. Also, we have given the graphical representations of the obtained results. These plots are useful in describing the dynamic characteristics of the solutions. The investigated equation is very essential in studying the mechanics of water waves and atmospheric predictability. Therefore, our techniques provide a great help in investigating various nonlinear models formulated in the contexts of fractional derivatives arising from oceanography and mathematical physics.
A new computational investigation to the new exact solutions of (3 + 1)-dimensional WKdV equations via two novel procedures arising in shallow water magnetohydrodynamics
(2022-01-01) Zhou M.; Akbulut A.; Kaplan M.; Kaabar M.K.A.; Yue X.G.
Various new exact solutions to (3 + 1)-dimensional Wazwaz-KdV equations are obtained in this work via two techniques: the modified Kudryashov procedure and modified simple equation method. The 3D plots, contour plots, and 2D plots of some obtained solutions are provided to describe the dynamic characteristics of the obtained solutions. Our employed techniques are very helpful in constructing new exact solutions to several nonlinear models encountered in ocean scientific phenomena arising in stratified flows, shallow water, plasma physics, and internal waves.
A novel investigation of exact solutions of the coupled nonlinear Schrodinger equations arising in ocean engineering, plasma waves, and nonlinear optics
(2022-01-01) Gu J.; Akbulut A.; Kaplan M.; Kaabar M.K.A.; Yue X.G.
We have analyzed the two coupled nonlinear Schrödinger equations (CNLSE) in the current work. This model has applications in high birefringence fibers. To generate different types of analytical solutions, including exponential, periodic, and soliton-type, we operated generalized Kudryashov, modified Kudryashov and exponential rational function procedures. Thanks to this implementation, we contributed to ocean engineering, plasma waves, nonlinear birefringence phenomena, and pulse compression features. In addition, in our article, we have included 2D and 3D graphics of solutions to help understand the physical meaning of solutions. The article highlights the method's ability to provide various solutions to various physical problems.
A unique computational investigation of the exact traveling wave solutions for the fractional-order Kaup-Boussinesq and generalized Hirota Satsuma coupled KdV systems arising from water waves and interaction of long waves
(2022-01-01) Wang X.; Yue X.G.; Kaabar M.K.A.; Akbulut A.; Kaplan M.
A novel technique, named auxiliary equation method, is applied in this research work for obtaining new traveling wave solutions for two interesting proposed systems: the Kaup-Boussinesq system and generalized Hirota-Satsuma coupled KdV system with beta time fractional derivative. Our solutions were obtained using MAPLE software. This technique shows a great potential to be applied in solving various nonlinear fractional differential equations arising from mathematical physics and ocean engineering. Since a standard equation has not been used as an auxiliary equation for this technique, different and novel solutions are obtained via this technique.
Dynamical investigation of time-fractional order Phi-4 equations
(2022-04-01) Younas H.M.; Iqbal S.; Siddique I.; Kaabar M.K.A.; Kaplan M.
In this manuscript, Optimal Homotopy Asymptotic Method (OHAM) is used to find the approximate solutions of time fractional Phi-4 nonlinear partial differential equations. Approximate first order results are acquired through OHAM and are compared with the exact solutions. It has been noticed that the obtained results from OHAM have large convergence rate for time-Fractional Order Partial Differential Equations. The solutions are plotted and therelative errors are tabulated.
Explicit iteration and unbounded solutions for fractional q–difference equations with boundary conditions on an infinite interval
(2022-01-01) Boutiara A.; Benbachir M.; Kaabar M.K.A.; Martínez F.; Samei M.E.; Kaplan M.
In this work, a proposed system of fractional boundary value problems is investigated concerning its unbounded solutions’ existence for a class of nonlinear fractional q-difference equations in the context of the Riemann–Liouville fractional q-derivative on an infinite interval. The system’s solution is formulated with the help of Green’s function. A compactness criterion is established in a special space. All the obtained results of uniqueness and existence are investigated with the help of fixed-point theorems. Some essential examples are illustrated to support our main outcomes.
Exploring new features for the (2+1)-dimensional Kundu–Mukherjee–Naskar equation via the techniques of (G^′/ G, 1 / G )-expansion and exponential rational function
(2023-01-01) Yue X.G.; Kaplan M.; Kaabar M.K.A.; Yang H.
The aim of the manuscript is to study new optical soliton solutions of the Kundu–Mukherjee–Naskar (KMN) equation via the (G′/ G, 1 / G )-expansion technique and the exponential rational function (ERF) procedure. The results are produced under the constraint conditions, and their graphical representation highlights them. These discoveries might aid in the comprehension of intricate nonlinear phenomena and oceanography. Studying the investigated equation in this paper is very important in explaining oceanographic phenomena such as rogue waves’ ocean currents.
Forecasting the dynamics of the model of cold bosonic atoms in a zig-zag optical lattice by symbolic computation
(2023-01-01) Yue X.G.; Shen Y.; Kaplan M.; Kaabar M.K.A.; Yang H.
The work aims to explore the exponential rational function technique and the generalized Kudryashov procedure to investigate one of the most important equations which is the equation of cold bosonic atoms in a zig-zag optical lattice. The considered equation is reduced to a supreme equation by using the continuum approximation which describes the soliton's dynamics with the implication pulse variables. The adopted techniques are accurate, simple, straightforward, and succinct to compute.
New approximate analytical solutions for the nonlinear fractional Schrödinger equation with second-order spatio-temporal dispersion via double Laplace transform method
(2021-09-30) Kaabar M.K.A.; Martínez F.; Gómez-Aguilar J.F.; Ghanbari B.; Kaplan M.; Günerhan H.
In this paper, a modified nonlinear Schrödinger equation with spatiotemporal dispersion is formulated in the senses of Caputo fractional derivative and conformable derivative. A new generalized double Laplace transform coupled with Adomian decomposition method has been defined and applied to solve the newly formulated nonlinear Schrödinger equation with spatiotemporal dispersion. The approximate analytical solutions are obtained and compared with each other graphically.
New conservation laws and exact solutions of the special case of the fifth-order KdV equation
(2022-08-01) Akbulut A.; Kaplan M.; Kaabar M.K.A.
The current study deals with the Kaup-Kupershmidt (KK) equation to construct formal Lagrangian, conservation laws, and exact solutions. KK is basically a special case of the 5th-order KdV equation. The conservation laws obtained by using the conservation theorem are trivial conservation laws. In addition, exact solutions are found via the modified simple equation (MSE) method. For a suitable value of solutions, the 3D surfaces have been plotted using MAPLE. These plots giving novel exact solutions are made to reveal important wave characteristics. Our obtained results in this work concerning our investigated equation are essential to explain many physical and oceanographic applications involving ocean gravity waves and many other related phenomena.
New exact soliton solutions of the (3 + 1)-dimensional conformable wazwaz-benjamin-bona-mahony equation via two novel techniques
(2021-01-01) Kaabar M.K.A.; Kaplan M.; Siri Z.
In this work, the (3 + 1)-dimensional Wazwaz-Benjamin-Bona-Mahony equation is formulated in the sense of conformable derivative. Two novel methods of generalized Kudryashov and exp(-φ(N) are investigated to obtain various exact soliton solutions. All algebraic computations are done with the help of the Maple software. Graphical representations are provided in 3D and 2D profiles to show the behavior and dynamics of all obtained solutions at various parameters' values and conformable orders using Wolfram Mathematica.
New exact solutions of the Mikhailov-Novikov-Wang equation via three novel techniques
(2023-01-01) Akbulut A.; Kaplan M.; Kaabar M.K.A.
The current work aims to present abundant families of the exact solutions of Mikhailov-Novikov-Wang equation via three different techniques. The adopted methods are generalized Kudryashov method (GKM), exponential rational function method (ERFM), and modified extended tanh-function method (METFM). Some plots of some presented new solutions are represented to exhibit wave characteristics. All results in this work are essential to understand the physical meaning and behavior of the investigated equation that sheds light on the importance of investigating various nonlinear wave phenomena in ocean engineering and physics. This equation provides new insights to understand the relationship between the integrability and water waves’ phenomena.
Novel exact solutions of the conformable resonant Schrödinger equation via two novel procedures with symbolic computational algorithms
(2023-01-01) Yue X.G.; Kaplan M.; Kaabar M.K.A.; Shen Y.
This study investigates novel exact solutions to the conformable resonant Schrödinger equation. For this purpose, two reliable techniques are employed involving the generalized Kudryashov and exponential rational function procedures. The 3D graphics of some obtained solutions are also given. The investigated equation is very important to the field of ocean engineering and science because many wave phenomena including water waves and rogue waves can be explained with the help of the nonlinear Schrödinger equation.
On some novel solution solutions to the generalized Schrödinger-Boussinesq equations for the interaction between complex short wave and real long wave envelope
(2022-08-01) Kumar D.; Hosseini K.; Kaabar M.K.A.; Kaplan M.; Salahshour S.
This paper explores some novel solutions to the generalized Schrödinger-Boussinesq (gSBq) equations, which describe the interaction between complex short wave and real long wave envelope. In order to derive some novel complex hyperbolic and complex trigonometric function solutions, the sine-Gordon equation method (sGEM) is applied to the gSBq equations. Novel complex hyperbolic and trigonometric function solutions are expressed by the dark, bright, combo dark-bright, W-shaped, M-shaped, singular, combo singular, and periodic wave solutions. The accuracy of the explored solitons is examined under the back substitution to the corresponding equations via the symbolic computation software Maple. It is found from the back substitution outcomes that all soliton solutions satisfy the original equations. The proper significance of the explored outcomes is demonstrated by the three-dimensional (3D) and two-dimensional (2D) graphs, which are presented under the selection of particular values of the free parameters. All the combo-soliton (W-shaped, M-shaped, and periodic wave) solutions are found to be new for the interaction between complex short wave and real long wave envelope in laser physics that show the novelty of the study. Moreover, the applied method provides an efficient tool for exploring novel soliton solutions, and it overcomes the complexities of the solitary wave ansatz method.