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Acta Mathematicae Applicatae Sinica 2016年第4期32卷 793-812页

作者： Elsayed M.E.ZAYED Yaser A.AMER Abdul-Ghani AL-NOWEHY Mathematics Department Faculty of SciencesZagazig University Mathematics Department Faculty of EducationAin Shams University

In this article, the fractional derivatives in the sense of the modified Riemann-Liouville derivatives together with the modified simple equation method and the multiple exp-function method are employed for constructing the exact solutions and the solitary wave solutions for the nonlinear time fractional Sharma-Tasso- Olver equation. With help of Maple, we can get exact explicit l-wave, 2-wave and 3-wave solutions, which include l-soliton, 2-soliton and 3-soliton type solutions if we use the multiple exp-function method while we can get only exact explicit l-wave solution including l-soliton type solution if we use the modified simple equation method. Two cases with specific values of the involved parameters are plotted for each 2-wave and 3-wave solutions.

关键词： modified simple equation method multiple exp-function method nonlinear fractional partialdifferential equations exact solution solitary wave solutions 1-wave solution 2-wave solution 3-wave solution

Exact Solutions of Kolmogorov-Petrovskii-Piskunov equation Using the modified simple equation method

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Acta Mathematicae Applicatae Sinica 2014年第3期30卷 749-754页

作者： E.M.E.Zayed S.A.Hoda Ibrahim Mathematics Department Faculty of ScienceZagazig University

The modified simple equation method is employed to find the exact solutions of the nonlinear Kolmogorov-Petrovskii-Piskunov （KPP） equation. When certain parameters of the equations are chosen to be special values, the solitary wave solutions are derived from the exact solutions. It is shown that the modified simple equation method provides an effective and powerful mathematical tool for solving nonlinear evolution equations in mathematical physics.

关键词： modified simple equation method Kolmogorov-Petrovskii-Piskunov equation exact solutions solitary wave solutions

Solitary Wave Solutions to the ZKBBM equation and the KPBBM equation via the modified simple equation method

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Journal of Partial Differential equations 2016年第2期29卷 143-160页

作者： AKTER J. AKBAR M. Ali Department of Natural Science Varendra University Bangladesh. Department of Applied Mathematics University of Rajshahi Bangladesh.

In this article, the modified simple equation method （MSE） is used to acquire exact solutions to nonlinear evolution equations （NLEEs） namely the Zakharov- Kuznetsov Benjamin-Bona-Mahony equation and the Kadomtsov-Petviashvilli Benjamin-Bona-Mahony equation which have widespread usage in modern science. The MSE method is ascending and useful mathematical tool for constructing exact travel- ing wave solutions to NLEEs in the field of science and engineering. By means of this method we attained some significant solutions with free parameters and for special values of these parameters, we found some soliton solutions derived from the exact solutions. The solutions obtained in this article have been shown graphically and also discussed physically.

关键词： modified simple equation method nonlinear evolution equations homogeneous balance soliton solutions Zakharov-Kuznetsov Benjamin-Bona-Mahony equation Kadomtsov- Petviashvilli Benjamin-Bona-Mahony equation.

N1-soliton solution for Schrodinger equation with competing weakly nonlocal and parabolic law nonlinearities

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Communications in Theoretical Physics 2020年第6期72卷 129-135页

作者： Mohammed O Al-Amr Hadi Rezazadeh Khalid K Ali Alper Korkmazki Department of Mathematics College of Computer Sciences and MathematicsUniversity of MosulMosul 41002Iraq Faculty of Engineering Technology Amol University of Special Modern TechnologiesAmolIran Mathematics Department Faculty of ScienceAl-Azhar UniversityNasr-CityCairoEgypt Nord StaBe 9 WeimarGermany

The nonlocal nonlinear Schr?dinger equation(NNLSE)with competing weakly nonlocal nonlinearity and parabolic law nonlinearity is explored in the current work.A powerful integration tool,which is a modified form of the simple equation method,is used to construct the dark and singular 1-soliton *** is shown that the modified simple equation method provides an effective and powerful mathematical gadget for solving various types of NNLSEs.

关键词： Schrodinger equation soliton integrability modified simple equation method

New conservation laws and exact solutions of the special case of the fifth-order KdV equation

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Journal of Ocean Engineering and Science 2022年第4期7卷 377-382页

作者： Arzu Akbulut Melike Kaplan Mohammed K.A.Kaabar Department of Mathematics-Computer Art-Science FacultyEskisehir Osmangazi UniversityEskisehirTurkey Department of Mathematics Art-Science FacultyKastamonu UniversityKastamonuTurkey Institute of Mathematical Sciences Faculty of ScienceUniversity of MalayaKuala Lumpur 50603Malaysia

The current study deals with the Kaup-Kupershmidt(KK)equation to construct formal Lagrangian,con-servation laws,and exact *** is basically a special case of the 5th-order KdV *** conservation laws obtained by using the conservation theorem are trivial conservation *** addition,exact solutions are found via the modified simple equation(MSE)*** a suitable value of solu-tions,the 3D surfaces have been plotted using *** plots giving novel exact solutions are made to reveal important wave *** 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.

关键词： Conservation laws Exact solutions Symbolic computation modified simple equation method

N1-soliton solution for Schr?dinger equation with competing weakly nonlocal and parabolic law nonlinearities

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Communications in Theoretical Physics 2020年第6期 131-137页

作者： Mohammed O Al-Amr Hadi Rezazadeh Khalid K Ali Alper Korkmazki Department of Mathematics College of Computer Sciences and Mathematics University of Mosul Faculty of Engineering Technology Amol University of Special Modern Technologies Mathematics Department Faculty of Science Al-Azhar University

The nonlocal nonlinear Schr?dinger equation(NNLSE) with competing weakly nonlocal nonlinearity and parabolic law nonlinearity is explored in the current work. A powerful integration tool, which is a modified form of the simple equation method, is used to construct the dark and singular 1-soliton solutions. It is shown that the modified simple equation method provides an effective and powerful mathematical gadget for solving various types of NNLSEs.

关键词： Schr?dinger equation soliton integrability modified simple equation method

On Solving the （2＋1）-Dimensional Nonlinear Cubic-Quintic Ginzburg-Landau equation Using Five Different Techniques

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Journal of Partial Differential equations 2018年第2期31卷 97-118页

作者： ZAYED Elsayed M. E. Al-NOWEHY A.-G. ELSHATER Mona E. M. Mathematics Department Faculty of Sciences Zagazig University P. O. Box 44519Zagazig Egypt. Mathematics Department Faculty of Education and Science Taiz University TaizYemen.

In this article, we apply five different techniques, namely the （G//G）-expansion method, an auxiliary equation method, the modified simple equation method, the first integral method and the Riccati equation method for constructing many new exact solutions with parameters as well as the bright-dark, singular and other soliton solutions of the （2＋1）-dimensional nonlinear cubic-quintic Ginzburg-Landau equation. Comparing the solutions of this nonlinear equation together with each other are presented. Comparing our new results obtained in this article with the well-known results are given too.

关键词： (G'/G)-expansion method auxiliary equation method modified simple equation method first integral method Riccati equation method exact traveling wave solutions solitary wave solutions Cubic-quintic Ginzburg-Landau equation.