Article
Materials Science, Multidisciplinary
Shao-Wen Yao, Asim Zafar, Aalia Urooj, Benish Tariq, Muhammad Shakeel, Mustafa Inc
Summary: This article examines the coupled KdV equations and the coupled system of variant Boussinesq equations with beta time derivative and explores their travelling wave solutions. This work explains the evolution of waves with fractional parameter. The simple ansatz approach produces a variety of novel solutions in terms of hyperbolic and periodic functions. Graphical representation of solutions are also presented.
RESULTS IN PHYSICS
(2023)
Article
Mathematics, Applied
Zhi-An Wang, Anita Yang, Kun Zhao
Summary: This paper investigates the existence and stability of traveling wave solutions of the Boussinesq-Burgers system, which describes the propagation of bores. By assuming weak dispersion of the fluid, we establish the existence of three different wave profiles using geometric singular perturbation theory and phase plane analysis. Furthermore, we prove the nonlinear asymptotic stability of the traveling wave solutions against small perturbations using the method of weighted energy estimates. Numerical simulations are conducted to showcase the generation and propagation of various wave profiles in both weak and strong dispersions, confirming our analytical results and showing that the Boussinesq-Burgers system can generate numerous propagating wave profiles depending on the profiles of initial data and the intensity of fluid dispersion.
PHYSICA D-NONLINEAR PHENOMENA
(2023)
Article
Mathematics
Lingxiao Li, Mingliang Wang, Jinliang Zhang
Summary: A generalized Logistic function is introduced to solve a first-order nonlinear ODE, successfully obtaining the traveling wave solutions of a class of nonlinear evolution equations including the generalized Fisher equation, the generalized Nagumo equation, etc.
Article
Mathematics, Applied
V. A. Shargatov, A. P. Chugainova
Summary: We investigated traveling wave solutions of a generalized Korteweg-de Vries-Burgers equation, where the dissipation coefficient has a smoothed step-like form and small-scale processes of dissipation and dispersion affect the solution in the high-gradient region. The solutions can converge to different limiting values, the flux function is non-convex with two inflection points, and the wave speed can have linearly stable solutions with different states behind them.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2021)
Article
Mathematics, Applied
Aiyong Chen, Chi Zhang, Wentao Huang
Summary: This study examines traveling wave solutions of a perturbed generalized KdV equation and proves that the limit wave speed is decreasing by analyzing the ratio of Abelian integrals. The upper and lower bounds of the limit wave speed are provided, partially addressing an open question previously proposed by Yan et al. (2014).
APPLIED MATHEMATICS LETTERS
(2021)
Article
Multidisciplinary Sciences
Abd-Allah Hyder, Mohamed A. Barakat, Ahmed H. Soliman, Areej A. Almoneef, Clemente Cesarano
Summary: In this paper, the coupled nonlinear KdV equations are solved in a stochastic environment by utilizing Hermite transforms, generalized conformable derivative, and a merging algorithm of white noise instruments and the (G'/G(2))-expansion technique. White noise functional conformable solutions for these equations are obtained. New stochastic periodic and soliton solutions for these equations under conformable generalized derivatives are produced. The obtained solutions exhibit controlled monotonicity and symmetry by assigning a value to the conformable parameter. A comparison between the obtained wave solutions and the wave solutions constructed under the conformable derivatives and Newton's derivatives is presented.
Article
Multidisciplinary Sciences
Xiaohua Zeng, Xiling Wu, Changzhou Liang, Chiping Yuan, Jieping Cai
Summary: The exact traveling wave solutions to coupled KdV equations with variable coefficients are obtained via the use of quadratic Jacobi's elliptic function expansion. The presented coupled KdV equations have a more general form than those studied in the literature. Nine couples of quadratic Jacobi's elliptic function solutions are found. Each couple of traveling wave solutions is symmetric in mathematical form. In the limit cases m ? 1, these periodic solutions degenerate as the corresponding soliton solutions. After the simple parameter substitution, the trigonometric function solutions are also obtained.
Article
Mathematics, Applied
Subhankar Sil, Partha Guha
Summary: This paper provides a geometric interpretation of the negative KdV equation and the Fuchssteiner equation and explores their symmetry and exact solutions through geometric methods such as projective connection. The paper also introduces traveling wave solutions and new exact solutions for the negative KdV equation, which are validated through numerical simulations.
JOURNAL OF GEOMETRY AND PHYSICS
(2022)
Article
Multidisciplinary Sciences
Jiaxin Shang, Wenhe Li, Da Li
Summary: This paper solves the coupled Schrodinger-Korteweg-de Vries equation using the generalized coupled trial equation method. A series of exact traveling wave solutions are obtained, including discontinuous periodic solutions, solitary wave solutions, and Jacobian elliptical function solutions. By drawing three-dimensional images of the modules of the solutions with Mathematica, the existence and properties of the solutions are determined. Compared to previous studies, more comprehensive and accurate solutions are obtained, giving the system more profound physical significance.
Article
Physics, Applied
Saima Arshed, Riaz Ur Rahman, Nauman Raza, Ahmad Kamal Khan, Mustafa Inc
Summary: This paper deals with optical solitons of fractional coupled Boussinesq, Burgers-type, and mKdV equations using the hypothesis of traveling wave and G'/G(2)-expansion scheme. The proposed method generates three distinct solutions, and the physical significance of the solutions is portrayed using graphical representations.
INTERNATIONAL JOURNAL OF MODERN PHYSICS B
(2022)
Article
Mathematics, Applied
Mustafa Inc, Unal Ic, Ibrahim Enam Inan, Jose Francisco Gomez-Aguilar
Summary: In this paper, a generalized (G'/G)-expansion method is implemented to solve some soliton wave equations and potential KdV equations. The solutions obtained include hyperbolic function solutions, trigonometric function solutions, exponential function solutions, and rational function solutions. The graphs of some solutions and numerical explanations are provided, and comparisons with previously found solutions are made using various methods.
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
(2022)
Article
Mathematics, Applied
Mehvish Fazal Ur Rehman, Yongyi Gu, Wenjun Yuan
Summary: The extended complex method has been successfully used to explore exact solutions for the generalized fifth-order KdV equation, obtaining rational, periodic, and elliptic function solutions. 3D graphs illustrate the physical phenomena related to the exact solutions of this equation. This method shows promise in acquiring exact solutions for various engineering differential equations.
JOURNAL OF FUNCTION SPACES
(2021)
Article
Mathematics, Applied
Baojian Hong, Jiaxin Zhou, Xingchen Zhu, Yiting Wang
Summary: In this work, novel optical solutions for the (1 + 1)-dimensional generalized M-fractional coupled nonlinear Schrodinger system (GMFCNLS) in various fields including ocean engineering, plasma waves, and nonlinear optics are investigated. Using modified expansion methods, different types of optical solutions such as bell-shape soliton solutions, blow-up solutions, periodic wave solutions, and mixed solitary wave solutions are obtained. These solutions are simulated and discussed to understand the system's inner structure.
JOURNAL OF FUNCTION SPACES
(2023)
Article
Thermodynamics
Mingshuo Liu, Lijun Zhang, Yong Fang, Huanhe Dong
Summary: This study explores the advantages of fractional derivative models over integer order models for fluids between elastic and viscous materials. Using the bilinear method, solutions to the time fractional Burgers equation and Boussinesq-Burgers equations for different fractional orders were derived, revealing properties such as time memory and increased oscillation frequency with higher fractional orders. The results suggest that fractional derivatives can enhance control performance in complex systems with fluids between different elastic and viscous materials.
Article
Mathematics, Applied
Aiyong Chen, Chi Zhang, Wentao Huang
Summary: This paper applies geometric singular perturbation theory to study the wave phenomena of a perturbed generalized KdV equation, proving the existence of solitary waves and periodic waves, as well as exploring the relationship between wave speed and wavelength.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S
(2023)
Article
Engineering, Multidisciplinary
Lama Sh. Aljoufi, M. B. Almatrafi, Aly R. Seadawy
Summary: This work discusses some natural phenomena in nonlinear sciences using discrete-time systems. It investigates the periodicity, boundedness, oscillation, stability, and exact solutions of nonlinear difference equations with generalized order. The stability of equilibrium points is examined using well-known theorems. Numerical examples are introduced to validate the theoretical work, implemented using MATLAB. The technique can also be applied to other rational recursive problems.
ALEXANDRIA ENGINEERING JOURNAL
(2023)
Article
Physics, Applied
Syed T. R. Rizvi, Aly R. Seadawy, Nimra, K. Ali, N. Aziz
Summary: This paper examines the soliton solutions of the Embedded Soliton (ES) generating model with a chi(2) nonlinear susceptibility. Using the sub-ODE technique, the bright, rational, Jacobi elliptic, periodic, dark, Weierstrass, and hyperbolic solitary wave solutions are found under certain conditions. The main objective of the sub-ODE method is to find wave solutions for complex models using simple and solvable ODEs called sub-ODEs. The resulting wave solutions are graphically presented for different parameter values.
INTERNATIONAL JOURNAL OF MODERN PHYSICS B
(2023)
Article
Multidisciplinary Sciences
Mounirah Areshi, Aly R. Seadawy, Asghar Ali, Abdulrahman F. AlJohani, Weam Alharbi, Amal F. Alharbi
Summary: Several types of solitary wave solutions of (3 + 1)-dimensional nonlinear extended and modified quantum Zakharov-Kuznetsov equations have been successfully established using three mathematical methods. These models have various applications in describing waves in quantum electron-positron-ion magnetoplasmas and weakly nonlinear ion-acoustic waves in plasma. The obtained results will be useful in studying the collaboration between lower nonlinear ion-acoustic waves and have significant implications in the field of mathematical physics.
Article
Mathematics, Applied
Aly R. Seadawy, Mujahid Iqbal
Summary: In this research work, we obtained the optical soliton solutions of the nonlinear complex Kundu-Eckhaus (KE) equation using a modified mathematical method. These solutions include dark solitons, bright solitons, combined dark-bright solitons, travelling wave solutions, and periodic wave solutions with general coefficients. These solutions are useful in various fields such as optical fiber development, soliton dynamics, adiabatic parameter dynamics, fluid dynamics, biomedical problems, and industrial phenomena. The technique used in this research proves to be powerful, effective, and fruitful for studying other higher-order nonlinear complex PDEs in fields like mathematical physics, quantum physics, geophysics, fluid mechanics, mathematical biology, engineering, and other physical sciences.
APPLIED MATHEMATICS-A JOURNAL OF CHINESE UNIVERSITIES SERIES B
(2023)
Article
Physics, Mathematical
Aly R. Seadawy, Syed T. R. Rizvi, Sarfaraz Ahmed
Summary: This template retrieves M-shaped rational solitons and their interactions with various types of solitons in optical fibers. The proposed equation compensates for small group velocity dispersion by including spatio-temporal dispersions of second and third orders. The new analytical solutions are found using symbolic computation and ansatz functions approach, and the stability characteristics of all solutions are also determined.
INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS
(2023)
Article
Physics, Applied
Syed T. R. Rizvi, Aly R. Seadawy, Sarfaraz Ahmed, Farrah Ashraf
Summary: This paper evaluates multiwave, homoclinic breather, M-shaped rational solitons and their interactions with single and double kinks for (1+1)-dimensional longitudinal wave equation using logarithmic transformation, symbolic computation, and ansatz functions method. Two types of M-shaped rational solitons are obtained and their dynamics are revealed through figures with different parameter values. Additionally, two forms of interaction between M-shaped rational soliton and kink wave are evaluated. Kink cross-rational solutions, periodic cross-rational solutions, generalized breathers, and Akhmediev breathers are also computed for the governing model. Soliton behaviors in the produced solutions with different parameter values are analyzed.
INTERNATIONAL JOURNAL OF MODERN PHYSICS B
(2023)
Article
Mathematics, Applied
Tahira Batool, Aly R. Seadawy, Syed T. R. Rizvi
Summary: In this article, various types of solutions for the Pavlov equation are derived, including lump solutions, solutions with I-kink and II-kink, periodic solutions, multiwave solutions, and rogue waves. The article also presents graphical representations of the solutions in three-dimensional, two-dimensional, and contour forms.
NONLINEAR ANALYSIS-MODELLING AND CONTROL
(2023)
Article
Physics, Multidisciplinary
Asghar Ali, Jamshad Ahmad, Sara Javed
Summary: In this paper, we used the modified (G') (G2-)expansion method and unified method to examine the novel complex solutions to the malaria model utilising the conformable derivative, which is an important biological concept. For the with-host malaria model, it is utilised to simulate the dynamics of malaria infection.
EUROPEAN PHYSICAL JOURNAL PLUS
(2023)
Article
Multidisciplinary Sciences
Jun Wang, Khurrem Shehzad, Aly R. Seadawy, Muhammad Arshad, Farwa Asmat
Summary: The aim of this paper is to further expand the use of the two-variable (G'/G,1/G)-expansion approach to a new coupled KdV and Z-K system, and construct different forms of analytical solutions. The stability of the solutions is examined, showing that this method has wide applications in engineering, etc.
JOURNAL OF TAIBAH UNIVERSITY FOR SCIENCE
(2023)
Article
Mathematics
Aly R. Seadawy, Syed T. R. Rizvi, Hanadi Zahed
Summary: In this study, various analytical rational solutions are explored using symbolic computation and ansatz transformation functions. Different types of rational solutions, such as M-shaped rational solutions, periodic cross-rational solutions, multi-wave solutions, rational kink cross-solutions, and homoclinic breather solutions, are obtained and their dynamics are visualized through the selection of appropriate parameter values. Additionally, two different types of interactions between M-shaped rational solutions and kink waves are analyzed. Furthermore, the stability of these solutions and the movement role of the wave are examined through the creation of graphs such as two-dimensional, three-dimensional, density, contour visual, and stream plots.
Article
Mathematics
Syed T. R. Rizvi, Aly R. Seadawy, Shami A. M. Alsallami
Summary: In this article, the improved perturbed nonlinear Schrodinger Equation (IP-NLSE) with dual power law nonlinearity is studied, which has applications in optical fibers and photovoltaic-photo-refractive materials. Grey and black optical solitons of the governing equation are found using a suitable complex envelope ansatz solution. Based on the Chupin Liu's theorem (CLT), new categories of combined optical soliton (COS) solutions to the IP-NLSE are evaluated. The propagation behaviors of homoclinic breathers (HB), multiwaves, and M-shape solitons are analytically examined.
Article
Physics, Mathematical
Muhammad Z. Baber, Aly R. Seadawy, Muhammad Qasim, Muhammad S. Iqbal, Syed T. R. Rizvi
Summary: This paper investigates the spatiotemporal structures of ratio-dependent prey and predator densities under different constraint conditions and suitable parameters, and the results show that the behavior and distribution of these densities vary with different parameter values.
INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS
(2023)
Article
Physics, Multidisciplinary
A. H. Tedjani, Aly R. Seadawy, Syed T. R. Rizvi, Emad Solouma
Summary: In this article, embedded solitons are discovered and their expressions are presented using Jacobi elliptic functions, allowing for graphical representation in both 2D and 3D forms.
EUROPEAN PHYSICAL JOURNAL PLUS
(2023)
Article
Mathematics
Shami A. M. Alsallami, Syed T. R. Rizvi, Aly R. Seadawy
Summary: We investigate the stochastic-fractional Drinfel'd-Sokolov-Wilson (SFDSW) equations for various wave solutions and interactions, including cross-kink rational waves, periodic cross-rational waves, homoclinic breather waves, M-shaped rational solutions, and M-shaped solutions with kink waves. These solutions have applications in mathematical physics, surface physics, plasma physics, population dynamics, and applied sciences. Graphical representations of the results are provided in different dimensions, obtained under certain constraint conditions.
Article
Mathematics, Interdisciplinary Applications
Mounirah Areshi, Aly R. Seadawy, Asghar Ali, Amal F. Alharbi, Abdulrahman F. Aljohani
Summary: This article investigates wave solutions of the Predator-Prey model with fractional derivative order using three modified mathematical methods. The derived solutions take the form of different functions such as trigonometric, hyperbolic, exponential, and rational functional. Some solutions are plotted in 2-dimensional and 3-dimensional by inserting specific values to attached parameters under sufficient condition on each solution for the physical phenomena of the fractional model. The proposed schemes are excellent mathematical tools for reviewing wave solutions of several fractional models in nonlinear science.
FRACTAL AND FRACTIONAL
(2023)
