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Applied Mathematics(A Journal of Chinese Universities) 2023年第1期38卷 16-26页

作者： aly r.seadawy Mujahid Iqbal Mathematics Department Faculty of ScienceTaibah UniversityAl-Madinah Al-Munawarah41411Kingdom of Saudi Arabia School of Mathematical Sciences Jiangsu UniversityZhenJiang 212013China

In this research work,we constructed the optical soliton solutions of nonlinear complex Kundu-Eckhaus(KE)equation with the help of modified mathematical *** obtained the solutions in the form of dark solitons,bright solitons and combined dark-bright solitons,travelling wave and periodic wave solutions with general *** our knowledge earlier reported results of the KE equation with specific *** obtained solutions are more useful in the development of optical fibers,dynamics of solitons,dynamics of adiabatic parameters,dynamics of fluid,problems of biomedical,industrial phenomena and many other *** calculations show that this technique is more powerful,effective,straightforward,and fruitfulness to study analytically other higher-order nonlinear complex PDEs involves in mathematical physics,quantum physics,Geo physics,fluid mechanics,hydrodynamics,mathematical biology,field of engineering and many other physical sciences.

关键词： Kundu-Eckhaus equation modified mathematical method solitons and solitary wave solutions

Dispersive soliton solutions for shallow water wave system and modified Benjamin-Bona-Mahony equations via applications of mathematical methods

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Journal of Ocean Engineering and Science 2021年第1期6卷 85-98页

作者： Asghar Ali aly r.seadawy Mathematics Department University of EducationLahorePakistan Mathematics Department Faculty of ScienceTaibah UniversityAl-Madinah Al-MunawarahSaudi Arabia

We have utilized three novel methods,called generalized direct algebraic,modified F-expansion and improved simple equation methods to construct traveling wave solutions of the system of shallow water wave equations and modified Benjamin-Bona-Mahony *** substituting particular values of the parameters,different solitary wave solutions are derived from the exact traveling wave *** is shown that these employed methods are more powerful tools for nonlinear wave equations.

关键词： System of shallow water wave equations Modified Benjamin-Bona-Mahony equation Generalized direct algebraic method Improved simple equation method Modified F-expansion method Traveling wave solutions Solitary wave solutions

Optical soliton and elliptic functions solutions of Sasa-satsuma dynamical equation and its applications

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Applied Mathematics(A Journal of Chinese Universities) 2021年第2期36卷 229-242页

作者： aly r.seadawy Naila Nasreen LU Dian-chen Mathematics department Faculty of scienceTaibah UniversityAI-Madinah Al-MunawarahSaudi Arabia Faculty of Science Jiangsu UniversityZhenjiang 212013China

The Sasa-satsuma(SS)dynamical equation interpret propagation of ultra-short and femto-second pulses in optical *** dynamical model has important physical *** this article,two mathematical techniques namely,improved F-expansion and improved aux-iliary methods are utilized to construct the several types of solitons such as dark soliton,bright soliton,periodic soliton,Elliptic function and solitary waves solutions of Sasa-satsuma dynamical *** results have imperative applications in sciences and other fields,and construc-tive to recognize the physical structure of this complex dynamical *** computing work and obtained results show the infuence and effectiveness of current methods.

关键词： Sasa-Satsuma equation improved F-expansion and auxiliary equation methods solitons elliptic function and periodic solutions

Stability Analysis of Solitary Wave Solutions for Coupled and(2+1)-Dimensional Cubic Klein-Gordon Equations and Their Applications

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Communications in Theoretical Physics 2018年第6期69卷 676-686页

作者： aly r.seadawy Dian-Chen Lu Muhammad Arshd Mathematics Department Faculty of ScienceTaibah UniversityTaibah UniversityA1-Madinah A1-MunawarahSaudi Arabia Mathematics Department Faculty of ScienceBeni-Suef UniversityEgypt Faculty of Science Jiangsu UniversityZhenjiang 212013China

The searching exact solutions in the solitary wave form of non-linear partial differential equations （PDEs） play a significant role to understand the internal mechanism of complex physical phenomena. In this paper we employ the proposed modified extended mapping method for constructing the exact solitary wave and soliton solutions of coupled Klein-Gordon equations and the （2-1-1）-dimensional cubic Klein-Gordon （K-G） equation. The Klein-Gordon equations are relativistic version of Schr6dinger equations, which describe the relation of relativistic energy-momentum in the form of quantized version. We productively achieve exact solutions involving parameters such as dark and bright solitary waves, Kink solitary wave, anti-Kink solitary wave, periodic solitary waves, and hyperbolic functions in which several solutions are novel. We plot the three-dimensional surface of some obtained solutions in this study. It is recognized that the modified mapping technique presents a more prestigious mathematical tool for acquiring analytical solutions of PDEs arise in mathematical physics.

关键词： modified extended mapping method coupled Klein-Gordon equation cubic Klein-Gordon equation solitons solitary wave solutions periodic solutions

Dispersive Solitary Wave Solutions of Strain Wave Dynamical Model and Its Stability

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Communications in Theoretical Physics 2019年第10期71卷 1155-1162页

作者： Muhammad Arshad aly r.seadawy Dian-Chen Lu Asghar Ali Faculty of Science Jiangsu UniversityZhenjiang 212013China Mathematics Department Faculty of ScienceTaibah UniversityAl-Madinah Al-MunawarahSaudi Arabia Department of Mathematics University of EducationMultan CampusPakistan

In the materials of micro-structured, the propagation of wave modeling should take into account the scale of various microstructures. The different kinds solitary wave solutions of strain wave dynamical model are derived via utilizing exp(-φ(ξ))-expansion and extended simple equation methods. This dynamical equation plays a key role in engineering and mathematical physics. Solutions obtained in this work include periodic solitary waves, Kink and antiKink solitary waves, bell-shaped solutions, solitons, and rational solutions. These exact solutions help researchers for knowing the physical phenomena of this wave equation. The stability of this dynamical model is examined via standard linear stability analysis, which authenticate that the model is stable and their solutions are exact. Graphs are depicted for knowing the movements of some solutions. The results show that the current methods, by the assist of symbolic calculation, give an effectual and direct mathematical tools for resolving the nonlinear problems in applied sciences.

关键词： exp(-∅(ξ))-expansion method improved simple equation method strain wave equation solitary waves periodic solutions

Propagation of traveling wave solutions to the Vakhnenko-Parkes dynamical equation via modified mathematical methods

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Applied Mathematics(A Journal of Chinese Universities) 2022年第1期37卷 21-34页

作者： aly r.seadawy Asghar Ali Wafaa A.Albarakati Dumitru Baleanu Mathematics department Faculty of scienceTaibah UniversityAl-Madinah Al-MunawarahSaudi Arabia Mathematics Department University of EducationLahoreMultan CampusPakistan Mathematics Department Faculty of scienceKing Abdulaziz UniversityJeddahSaudi Arabia Department of Mathematics Cankaya UniversityAnkaraTurkey

In this paper, we investigate some new traveling wave solutions to Vakhnenko-Parkes equation via three modified mathematical methods. The derived solutions have been obtained including periodic and solitons solutions in the form of trigonometric, hyperbolic, and rational function solutions. The graphical representations of some solutions by assigning particular values to the parameters under prescribed conditions in each solutions and comparing of solutions with those gained by other authors indicate that these employed techniques are more effective, efficient and applicable mathematical tools for solving nonlinear problems in applied science.

关键词： Vakhnenko-Parkes equation(VPE) generalized direct algebraic method extended simple equation method modified F-expansion method

Solitary wave solutions for the generalized Zakharov-Kuznetsov-Benjamin-Bona-Mahony nonlinear evolution equation

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Journal of Ocean Engineering and Science 2017年第2期2卷 137-142页

作者： aly r.seadawy Dianchen Lu Mostafa M.A.Khater Department of Mathematics Faculty of ScienceTaibah UniversityAl-UlaSaudi Arabia Department of Mathematics Faculty of ScienceJiangsu UniversityChina Department of Mathematics Faculty of ScienceMansoura University35516 MansouraEgypt

In this paper,we utilize the exp(−ϕ(ξ))-expansion method to find exact and solitary wave solutions of the generalized Zakharov-Kuznetsov-Benjamin-Bona-Mahony nonlinear evolution *** generalized Zakharov-Kuznetsov-Benjamin-Bona-Mahony nonlinear evolution equation describes the model for the propagation of long waves that mingle with nonlinear and dissipative *** model is used in the analysis of the surface waves of long wavelength in hydro magnetic waves in cold plasma,liquids,acoustic waves in harmonic crystals and acoustic-gravity waves in compressible *** using this method,seven different kinds of traveling wave solutions are successfully obtained for this *** considered method and transformation techniques are efficient and consistent for solving nonlinear evolution equations and obtain exact solutions that are applied to the science and engineering fields.

关键词： The exp(−ϕ(ξ))-expansion method The generalized Zakharov-Kuznetsov-Benjamin-Bona-Mahony nonlinear evolution equation Traveling wave solutions Solitary wave solutions

Generalized solitary wave solutions to the time fractional generalized Hirota-Satsuma coupled KdV via new definition for wave transformation

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Journal of Ocean Engineering and Science 2019年第2期4卷 77-84页

作者： Hadi rezazadeh aly r.seadawy Mostafa Eslami Mohammad Mirzazadeh Faculty of Modern Technologies Engineering Amol University of Special Modern TechnologiesAmolIran Mathematics Department Faculty of ScienceTaibah UniversityAl-MadinahAl-MunawarahSaudi Arabia Mathematics Department Faculty of ScienceBeni-Suef UniversityEgypt Department of Mathematics Faculty of Mathematical SciencesUniversity of MazandaranBabolsarIran Department of Engineering Sciences Faculty of Technology and EngineeringEast of GuilanUniversity of GuilanRudsar-VajargahIran

In this paper,the(G′/G)-expansion method has been applied to explore new solitary wave solutions for the time fractional generalized Hirota-Satsuma coupled KdV(FGHSC KdV)*** fractional derivative is described with the use of conformable *** results show that this method is a very useful and effective mathematical tool for solving nonlinear conformable fractional equations arising in mathematical *** a result,this method can also be applied to other nonlinear conformable fractional differential equations.©2019 Shanghai Jiaotong *** by Elsevier B.V.

关键词： Conformable fractional derivative (G′/G)-expansion method Solitary wave solutions Time fractional generalized Hirota-Satsuma coupled KdV system.

Stability analysis solutions of the nonlinear modified Degasperis-Procesi water wave equation

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Journal of Ocean Engineering and Science 2017年第3期2卷 155-160页

作者： M.A.Helal aly r.seadawy M.Zekry Mathematics Department Faculty of ScienceCairo UniversityGizaEgypt Mathematics Department Faculty of ScienceTaibah UniversityAl-UlaSaudi Arabia Mathematics Department Faculty of ScienceBeni-Suef UniversityEgypt

In the present study,the solitary wave solutions of modified Degasperis-Procesi equation are *** the standard Degasperis-Procesi equation,where multi-peakon solutions arise,the modification caused a change in the characteristic of these peakon solutions and changed it to bell-shaped *** using the extended auxiliary equation method,we deduced some new soliton solutions of the fourthorder nonlinear modified Degasperis-Procesi equation with constant *** solutions include symmetrical,non-symmetrical kink solutions,solitary pattern solutions,weiestrass elliptic function solutions and triangular function *** discuss the stability analysis for these solutions.

关键词： Modified Degasperis-Procesi water wave equation Extended auxiliary equation method Solitary wave solutions

A variety of novel closed-form soliton solutions to the family of Boussinesq-like equations with different types

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Journal of Ocean Engineering and Science 2022年第6期7卷 543-554页

作者： Dipankar Kumar Gour Chandra Paul aly r.seadawy M.T.Darvishi Department of Mathematics Bangabandhu Sheikh Mujibur Rahman Science and Technology UniversityGopalganj 8100Bangladesh Department of Mathematics University of RajshahiRajshahi 6205Bangladesh Mathematics Department Faculty of ScienceTaibah UniversityAl-Madinah Al-MunawarahSaudi Arabia Mathematics Department Faculty of ScienceBeni–Suef UniversityBeni SuefEgypt Department of Mathematics Razi UniversityKermanshah 67149Iran

This paper deals with the closed-form solutions to the family of Boussinesq-like equations with the effect of spatio-temporal *** sine-Gordon expansion and the hyperbolic function approaches are efficiently applied to the family of Boussinesq-like equations to explore novel solitary,kink,anti-kink,combo,and singular-periodic wave *** attained solutions are expressed by the trigonometric and hyperbolic functions including tan,sec,cot,csc,tanh,sech,coth,csch,and of their *** addition,the mentioned two approaches are applied to the aforesaid models in the sense of Atangana conformable derivative or Beta derivative to attain new wave ***-dimensional and two-dimensional graphs of some of the obtained novel solutions satisfying the corresponding equations of interest are provided to understand the underlying mechanisms of the stated *** the bright wave solutions in terms of Atangana’s conformable derivative,the amplitudes of the bright wave gradually decrease,but the smoothness increases when the fractional parametersαandβ*** the other hand,the periodicities of periodic waves *** attained new wave solutions can motivate applied scientists for engineering their ideas to an optimal level and they can be used for the validation of numerical simulation results in the propagation of waves in shallow water and other nonlinear *** performed approaches are found to be simple and efficient enough to estimate the solutions attained in the study and can be used to solve various classes of nonlinear partial differential equations arising in mathematical physics and engineering.

关键词： Boussinesq-like equations The sine-Gordon expansion approach The hyperbolic function approach Wave solutions Atangana conformable derivative