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EXPONENTIAL ATTRACTOR FOR THE GENERALIZED symmetric regularized long wave equation WITH DAMPING TERM

Applied Mathematics and Mechanics(English Edition) 2005年第3期26卷 283-291页

作者：尚亚东郭柏灵 School of Mathematics and Information Science Guangzhou UniversityGuangzhou 510405 P.R.China Institute of Applied Physics and Computational Mathematics P.O.Box 8009 Beijing 100088 P.R.China

The global fast dynamics for the generalized symmetric regularized long wave equation with damping term is considered. The squeezing property of the nonlinear semi_group associated with this equation and the existence... 详细信息

关键词： symmetric regularized long wave equation asymptotic behavior squeezing property exponential attractor

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FINITE DIMENSIONAL BEHAVIOR FOR THE DISSIPATIVE GENERALIZED symmetric regularized long wave equationS

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Journal of Systems Science & Complexity 2003年第2期16卷 236-248页

作者： SHANGYadong GUOBoling DepavtmentofMathematics GuangzhouUniversityGuangzhou510405China InstituteofAppliedPhysicsandComputationalMathematics P.O.Box8009Beijing100088China

This paper deals with the asymptotic behaviour of solutions for thegeneralized symmetric regularized long wave equations with dissipation term. We first show theexistence of global weak attractors for the periodic initial value problem of this equations in H^2x H^1. And then by an energy equation and an idea of Ghidaglia and Guo, we conclude that the globalweak attractor is actually the global strong attractor for S(t) in H^2 (Ω) x H^1 (Ω). The finitedimensionality of the global attractor is also established.

关键词： symmetric regularized long wave equation periodic initial value problem global attractors hausdorff dimension fractal dimension

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解高维广义对称正则长波方程的Fourier谱方法

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高等学校计算数学学报 1999年第1期21卷 48-60页

作者：尚亚东李志深兰州大学数学系!兰州　730000 西安石油学院基础部!西安　710065

In this paper, we consider the periodic initial value problem for one class of system of higher multidimensional generalized symmetric regularized long wave equations. The semi-discrete and full-discrete Fourier Galerkin spetral schemes are constructed for the problem. The L2-norm and H1-norm convergence results and the error estimate are proved in theory.

关键词： symmetric regularized long wave equation periodic inttial value problem spetral method error estimates

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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

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Soliton solutions for time fractional ocean engineering models with Beta derivative

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Journal of Ocean Engineering and Science 2022年第5期7卷 444-448页

作者： Ibrahim Yalçınkaya Hijaz Ahmad Orkun Tasbozan Ali Kurt Department of Mathematics and Computer Sciences Faculty of ScienceNecmettin Erbakan UniversityKonyaTurkey Department of Basic Sciences University of Engineering and TechnologyPeshawarPakistan Department of Mathematics Faculty of Science and LiteratureHatay Mustafa Kemal UniversityHatayTurkey Department of Mathematics Faculty of Science and LiteraturePamukkale UniversityDenizliTurkey

In this study,the authors obtained the soliton and periodic wave solutions for time fractional symmetric regularized long wave equation(SRLW)and Ostrovsky equation(OE)both arising as a model in ocean *** this aim modified extended tanh-function(mETF)is *** using this method,chain rule is employed to turn fractional nonlinear partial differential equation into the nonlinear ordinary differential equation in integer *** to the chain rule,there is no further requirement for any normalization or *** derivative which involves fractional term is used in considered mathematical *** the exact solutions of these equations is very important for knowing the wave behavior in ocean engineering models.

关键词： symmetric regularized long wave equation Beta derivative Ostrovsky equation Analytical solution Soliton solutions Periodic wave solution

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