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Journal of Partial Differential Equations 2015年第4期28卷 332-357页

作者： ZAYED E. M. E. ALURRFI K. A. E. Department of Mathematics Faculty of Science Zagazig University P. O. Box 44519Zagazig Egypt

The propagation of the optical solitons is usually governed by the nonlinear Schrodinger equations. In this article, the two variable （G＇/G,1/G）-expansion method is employed to construct exact traveling wave solutions with parameters of two higher order nonlinear Schrodinger equations describing the propagation of femtosecond pulses in nonlinear optical fibers. When the parameters are replaced by special values, the well-known solitary wave solutions of these equations rediscovered from the traveling waves. This method can be thought of as the generalization of well-known original （G＇/G）-expansion method proposed by M. Wang et al. It is shown that the two variable （G＇/G,1/G）-expansion method provides a more powerful mathematical tool for solving many other nonlinear PDEs in mathematical physics.

关键词： The two variable (G'/G,1/G)-expansion method Schrodinger equations exact traveling wave solutions Solitary wave solutions.

Further investigations to extract abundant new exact traveling wave solutions of some NLEEs

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Journal of Ocean Engineering and Science 2019年第4期4卷 387-394页

作者： M.Mamun Miah Aly R.Seadawy H.M.Shahadat Ali M.Ali Akbar Department of Mathematics Khulna University of Engineering and TechnologyBangladesh Mathematics Department Taibah UniversityAl-Madinah Al-MunawarahSaudi Arabia Department of Mathematics Beni-Suef UniversityEgypt Department of Applied Mathematics Noakhali Science and Technology UniversityBangladesh Department of Applied Mathematics University of RajshahiRajshahi-6205Bangladesh

In this study,we implement the generalized(G/G)-expansion method established by Wang et *** examine wave solutions to some nonlinear evolution *** method,known as the double(G/G,1/G)-expansion method is used to establish abundant new and further general exact wave solutions to the(3+1)-dimensional Jimbo-Miwa equation,the(3+1)-dimensional Kadomtsev-Petviashvili equation and symmetric regularized long wave *** solutions are extracted in terms of hyperbolic function,trigonometric function and rational *** solitary wave solutions are constructed from the obtained traveling wave solutions if the parameters received some definite *** of the solutions are also depicted to describe the phenomena apparently and the shapes of the obtained solutions are singular periodic,anti-kink,singular soliton,singular anti-bell shape,compaction *** method is straightforward,compact and reliable and gives huge new closed form traveling wave solutions of nonlinear evolution equations in ocean engineering.

关键词： exact traveling wave solutions (G/G,1/G)-expansion method (3+1)-dimensional Jimbo-Miwa equation (3+1)-dimensional Kadomtsev-Petviashvili equation Symmetric regularized long wave equation

exact traveling wave solutions of （3+1）-dimensional Kadomtsev-Petviashvili Equation

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Exact Traveling Wave Solutions of （3+1）-dimensional Kadomt...

New exact traveling wave solutions of (2 + 1)-Dimensional Time-Fractional Zoomeron Equation

作者： Wan-rong XU Li-feng GUO School of Mathematics and Statistics Northeast Petroleum University

By transforming the （3+1）-dimensional nonlinear Kadomtsev-Petviashvili equation into an elementary integral form,the exact traveling wave solutions of （3+1）-dimensional nonlinear KP equation are obtained by using ... 详细信息

关键词： KP equation Complete discrimination system of polynomial exact traveling wave solutions

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Journal of Applied Mathematics and Physics 2022年第2期10卷 333-346页

作者： Zhiyun Zeng Xiaohua Liu Yin Zhu Xue Huang College of Data Science and Information Engineering Guizhou Minzu University Guiyang China

In this paper, the new mapping approach and the new extended auxiliary equation approach were used to investigate the exact traveling wave solutions of (2 + 1)-dimensional time-fractional Zoomeron equation with the conformable fractional derivative. As a result, the singular soliton solutions, kink and anti-kink soliton solutions, periodic function soliton solutions, Jacobi elliptic function solutions and hyperbolic function solutions of (2 + 1)-dimensional time-fractional Zoomeron equation were obtained. Finally, the 3D and 2D graphs of some solutions were drawn by setting the suitable values of parameters with Maple, and analyze the dynamic behaviors of the solutions.

关键词： exact traveling wave solutions (2 + 1)-Dimensional Time-Fractional Zoomeron Equation The New Mapping Approach The New Extended Auxiliary Equation Approach

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.

solutions and Bifurcations of a class of (3+1)-dimensional Nonlinear Models generated by the Jaulent-Miodek hierarchy equation

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Solutions and Bifurcations of a class of (3+1)-dimensional N...