Browsing by Author "Yue X.G."

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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.
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.
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.