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Journal of Ocean Engineering and Science 2024年第3期9卷 207-215页

作者： Khalid K.Ali M.S.Mehanna Abdel-Haleem Abdel-Aty abdul-majid wazwaz Department of Mathematics Faculty of ScienceAl-Azhar UniversityNasr City 11884CairoEgypt Faculty of Engineering MTI UniversityCairoEgypt Department of Physics College of SciencesUniversity of BishaPO Box 344Bisha 61922Saudi Arabia Physics Department Faculty of ScienceAl-Azhar UniversityAssiut 71524Egypt Department of Mathematics Saint Xavier UniversityChicagoIL 60655USA

In this article,we suggest a new form of modified Kudryashov’s method(NMK)to study the Dual-mode Sawada Kotera *** know very well that the more the solutions depend on many constants,the easier it is to study the model better by observing the change in the constants and what their impact is on the *** this point of view,we developed the modified Kudryashov method and put it in a general form that contains more than one controllable *** have studied the model in this way and presented figures showing the correctness of what we hoped to reach from the proposed *** addition to the results we reached,they were not sufficient,so we presented an extensive numerical study of this model using the finite differences *** also came up with the local truncation error for the difference scheme is h^(6) k^(2)(1+k^(2)).In addition,the analytical solutions we reached were compared with the numerical solutions,and we presented many forms that show that the results we reached are a clear contribution to this field.

关键词： Soliton solution A new form of analytical method Local truncation error Numerical solutions

Perturbation,symmetry analysis,Bäcklund and reciprocal transformation for the extended Boussinesq equation in fluid mechanics

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Communications in Theoretical Physics 2021年第4期73卷 21-28页

作者： Gangwei Wang abdul-majid wazwaz School of Mathematics and Statistics Hebei University of Economics and BusinessShijiazhuang050061China Department of Mathematics Saint Xavier UniversityChicagoIL 60655United States of America

In this work,we study a generalized double dispersion Boussinesq equation that plays a significant role in fluid mechanics,scientific fields,and ocean *** equation will be reduced to the Korteweg-de Vries equation via using the perturbation *** derive the corresponding vectors,symmetry reduction and explicit solutions for this *** readily obtain Bäcklund transformation associated with truncated Painlevé*** also examine the related conservation laws of this equation via using the multiplier ***,we investigate the reciprocal Bäcklund transformations of the derived conservation laws for the first time.

关键词： Boussinesq equation perturbation and symmetry analysis Bäcklund transformation conservation laws

A New Integrable (2+1)-Dimensional Generalized Breaking Soliton Equation:N-Soliton Solutions and Traveling Wave Solutions

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Communications in Theoretical Physics 2016年第10期65卷 385-388页

作者： abdul-majid wazwaz Department of Mathematics Saint Xavier University

In this work,we study a new(2+1)-dimensional generalized breaking soliton equation which admits the Painleve property for one special set of *** derive multiple soliton solutions,traveling wave solutions,and periodic ... 详细信息

关键词： breaking soliton equations Hirota bilinear method multiple soliton solutions traveling wave solutions

The simplified Hirota’s method for studying three extended higher-order KdV-type equations

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Journal of Ocean Engineering and Science 2016年第3期1卷 181-185页

作者： abdul-majid wazwaz Department of Mathematics Saint Xavier UniversityChicagoIL 60655USA

In this work we study three extended higher-order KdV-type *** Lax-type equation,the Sawada-Kotera-type equation and the CDG-type equation are derived from the extended KdV *** use the simplified Hirota’s direct method to derive multiple soliton solutions for each *** show that each model gives multiple soliton solutions,where the structures of the obtained solutions differ from the solutions of the canonical form of these equations.

关键词： Fifth-order KdV equation Hirota’s method Dispersion relation

A new integrable nonlocal modified KdV equation:Abundant solutions with distinct physical structures

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Journal of Ocean Engineering and Science 2017年第1期2卷 1-4页

作者： abdul-majid wazwaz Department of Mathematics Saint Xavier UniversityChicagoIL 60655United States

In this work we study a new integrable nonlocal modified Korteweg-de Vries equation(mKdV)which arises from a reduction of the AKNS scattering *** use a variety of distinct techniques to determine abundant solutions with distinct physical *** show that this nonlocal equation possesses a family of traveling solitary wave solutions that include solitons,kinks,periodic and singular solutions.

关键词： Nonlocal modified KdV equation Soliton solutions Periodic solutions Exponential solutions

A reliable analysis of oxygen diffusion in a spherical cell with nonlinear oxygen uptake kinetics

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International Journal of Biomathematics 2014年第2期7卷 165-176页

作者： Randolph Rach abdul-majid wazwaz Jun-Sheng Duan 316 S. Maple St.Hartford MI 49057-1225 USA Department of Mathematics Saint Xavier University Chicago IL 60655 USA School of SciencesShanghai Institute of Technology Shanghai 201418 P. R. China

In this paper, we investigate the diffusion of oxygen in a spherical cell including nonlin- ear uptake kinetics. The Lane-Emden boundary value problem with Michaelis-Menten kinetics is used to model the dimensionless oxygen concentration in our analysis. We first convert the Lane-Emden equation to the equivalent Volterra integral form that incorporates the boundary condition at the cell＇s center, but which still leaves one unknown constant of integration, as an intermediate step. Next we evaluate the Volterra integral form of the concentration and its flux at the cell membrane and substitute them into the remaining boundary condition to determine the unknown constant of integration by appropriate algebraic manipulations. Upon substitution we have converted the equivalent Volterra integral form to the equivalent Fredholm Volterra integral form, and use the Duan Rach modified recursion scheme to effectively decompose the unknown constant of integration by formula. The Adomian decomposition method is then applied to solve the equivalent nonlinear Fredholm-Volterra integral representation of the LaneEmden model for the concentration of oxygen within the spherical cell. Our approach shows enhancements over existing techniques.

关键词： Oxygen diffusion Volterra integral form Michaelis-Menten kinetics Adomian decomposition method Adomian polynomials.

Hypergeometric Series Solution to a Class of Second-Order Boundary Value Problems via Laplace Transform with Applications to Nanofluids

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Communications in Theoretical Physics 2017年第3期67卷 231-234页

作者： Abdelhalim Ebaid abdul-majid wazwaz Elham Alali Basem S.Masaedeh Department of Mathematics Faculty of Science University of Tabuk P.O. Box 741 Tabuk 71491 Saudi Arabia Department of Mathematics and Computer Science Saint Xavier University Chicago IL 60655 USA

Very recently, it was observed that the temperature of nanofluids is finally governed by second-order ordinary differential equations with variable coefficients of exponential orders. Such coefficients were then transformed to polynomials type by using new independent variables. In this paper, a class of second-order ordinary differential equations with variable coefficients of polynomials type has been solved analytically. The analytical solution is expressed in terms of a hypergeometric function with generalized parameters. Moreover, applications of the present results have been applied on some selected nanofluids problems in the literature. The exact solutions in the literature were derived as special cases of our generalized analytical solution.

关键词： ordinary differential equation hypergeometric series boundary value problem exact solution Laplace transform nanofluid

Perturbation, symmetry analysis, B?cklund and reciprocal transformation for the extended Boussinesq equation in fluid mechanics

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Communications in Theoretical Physics 2021年第4期73卷 25-32页

作者： Gangwei Wang abdul-majid wazwaz School of Mathematics and Statistics Hebei University of Economics and Business Department of Mathematics Saint Xavier University Chicago

In this work, we study a generalized double dispersion Boussinesq equation that plays a significant role in fluid mechanics, scientific fields, and ocean engineering. This equation will be reduced to the Korteweg–de Vries equation via using the perturbation analysis. We derive the corresponding vectors, symmetry reduction and explicit solutions for this equation. We readily obtain B?cklund transformation associated with truncated Painlevéexpansion. We also examine the related conservation laws of this equation via using the multiplier method. Moreover, we investigate the reciprocal B?cklund transformations of the derived conservation laws for the first time.

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New Painlevé Integrable(3+1)-Dimensional Combined pKP–BKP Equation:Lump and Multiple Soliton Solutions

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Chinese Physics Letters 2023年第12期40卷 19-26页

作者： abdul-majid wazwaz Department of Mathematics Saint Xavier UniversityChicagoIL 60655USA

We introduce a new form of the Painlevé integrable(3+1)-dimensional combined potential Kadomtsev–Petviashvili equation incorporating the B-type Kadomtsev–Petviashvili equation(pKP–BKP equation). We perform the Painlevé analysis to emphasize the complete integrability of this new(3+1)-dimensional combined integrable equation. We formally derive multiple soliton solutions via employing the simplified Hirota bilinear method. Moreover, a variety of lump solutions are determined. We also develop two new(3+1)-dimensional pKP–BKP equations via deleting some terms from the original form of the combined p KP–BKP equation. We emphasize the Painlevé integrability of the newly developed equations, where multiple soliton solutions and lump solutions are derived as well. The derived solutions for all examined models are all depicted through Maple software.

关键词： equation method integrable

Dynamics of lump chains for the BKP equation describing propagation of nonlinear waves

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Chinese Physics B 2023年第4期32卷 226-236页

作者：赵忠龙和玲超 abdul-majid wazwaz School of Mathematics North University of ChinaTaiyuan 030051China College of Mathematics Taiyuan University of TechnologyTaiyuan 030024China Department of Mathematics Saint Xavier UniversityChicagoIL 60655USA

A large member of lump chain solutions of the(2+1)-dimensional Bogoyavlenskii-Kadomtsev-Petviashvili(BKP)equation are constructed by means of theτ-function in the form of *** lump chains are formed by periodic arrangement of individual lumps and travel with distinct group and *** analytical method related dominant regions of polygon is developed to analyze the interaction dynamics of the multiple lump *** degenerate structures of parallel,superimposed,and molecular lump chains are *** interaction solutions between lump chains and kink-solitons are investigated,where the kink-solitons lie on the boundaries of dominant region determined by the constant term in theτ-***,the hybrid solutions consisting of lump chains and individual lumps controlled by the parameter with high rank and depth are *** analytical method presented in this paper can be further extended to other integrable systems to explore complex wave structures.

关键词： lump chains interaction solutions BKP equation