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Numerical Solution of Nonlinear System of Partial Differential Equations by the Laplace Decomposition Method and the Pade Approximation

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American Journal of Computational Mathematics 2013年第3期3卷 175-184页

作者： Magdy Ahmed Mohamed Mohamed Shibl Torky Faculty of Science Suez Canal University Ismailia Egypt The High Institute of Administration and Computer Port Said University Port Said Egypt

In this paper, Laplace decomposition method (LDM) and Pade approximant are employed to find approximate solutions for the Whitham-Broer-Kaup shallow water model, the coupled nonlinear reaction diffusion equations and the system of Hirota-Satsuma coupled kdv. In addition, the results obtained from Laplace decomposition method (LDM) and Pade approximant are compared with corresponding exact analytical solutions.

关键词： Nonlinear System of Partial Differential Equations The Laplace Decomposition Method The Pade Approximation The Coupled System of the Approximate Equations for Long Water Waves The Whitham Broer Kaup Shallow Water Model The System of Hirota-Satsuma Coupled kdv

Modified Adomain Decomposition Method for the Generalized Fifth Order kdv Equations

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American Journal of Computational Mathematics 2013年第1期3卷 53-58页

作者： Huda O. Bakodah Department of Mathematics Science Faculty for Girls King Abdulaziz University Jeddah KSA

New modified Adomian decomposition method is proposed for the solution of the generalized fifth-order Korteweg-de Vries (GFkdv) equation. The numerical solutions are compared with the standard Adomian decomposition method and the exact solutions. The results are demonstrated which confirm the efficiency and applicability of the method.

关键词： Modified Adomian Decomposition Method Fifth Order kdv Equation Solitary-Wave Solution

Homotopy Perturbation Method for the Generalized Hirota-Satsuma Coupled kdv Equation

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Applied Mathematics 2012年第12期3卷 1983-1989页

作者： Dalal A. Maturi Department of Mathematics Faculty of Science King AbdulAziz University Jeddah Saudi Arabia

In this paper, we consider the homotopy perturbation method (HPM) to obtain the exact solution of Hirota-Satsuma Coupled kdv equation. The results reveal that the proposed method is very effective and simple and can b... 详细信息

关键词： Homotopy Perturbation Method Generalized Hirota-Satsuma Coupled kdv Equation

Numerical Solution of Kortweg-de Vries Equation

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Applied Mathematics 2020年第4期11卷 344-362页

作者： Fakhirah Alotaibi M. S. Ismail Dept. of Math King Abdulaziz University Jeddah Saudi Arabia

In this paper, we are going to derive numerical methods for solving the kdv equation using Pade approximation for space direction, trapezoidal and implicit mid-point rule in the time direction. The schemes will be analyzed for accuracy and stability. The exact solution and the conserved quantities will be used to display the efficiency and the robustness of the proposed schemes. Interaction of two and three solitons will be conducted. The numerical results showed, interaction behavior is elastic and the conserved quantities are conserved which is a good indication of the reliability of the schemes under consideration.

关键词： kdv Soliton Pade Approximation Numerical Schemes Interaction of Solitons

一类广义kdv方程的多重守恒格式及其理论分析方法

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高等学校计算数学学报 1994年第1期16卷 1-13页

作者：贺国强上海科技大学

1 引言不少描述波动或其它运动现象的非线性方程有多个守恒律,例如Korteweg-deVries(kdv)方程有无限个守恒律。用数值方法求解这些方程时,一个自然的想法是离散模拟这些守恒律,若能同时模拟多个守恒律,那就更吸引人了。对于kdv方程,已有

关键词：方程 kdv 守恒格式差分格式正则解分析方法广义

Pulse Soliton Solutions of the Modified kdv and Born-Infeld Equations

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International Journal of Modern Nonlinear Theory and Application 2013年第2期2卷 135-140页

作者： Jean Roger Bogning Department of Physics Higher Teacher’s Training College Bambili University of Bamenda Bamenda Cameroon

In this work, we use the Bogning-Djeumen Tchaho-Kofané method to look for all solutions of shape Sechn- of the modified kdv and Born-Infeld Equations. n being a real number, we obtain the soliton solutions when n is ... 详细信息

关键词： kdv Equation Born-Infeld Equation Soliton Solution BDKm Modified kdv Equation

Existence the Solutions of Some Fifth-Order kdv Equation by Laplace Decomposition Method

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American Journal of Computational Mathematics 2013年第1期3卷 80-85页

作者： Sujit Handibag B. D. Karande Department of Mathematics Maharashtra Udaygiri Mahavidyalaya Udgir India Department of Mathematics Mahatma Basweshwar Mahavidyalaya Latur India

In this paper, we develop a method to calculate numerical and approximate solution of some fifth-order Korteweg-de Vries equations with initial condition with the help of Laplace Decomposition Method (LDM). The technique is based on the application of Laplace transform to some fifth-order kdv equations. The nonlinear term can easily be handled with the help of Adomian polynomials. We illustrate this technique with the help of four examples and results of the present technique have closed agreement with approximate solutions obtained with the help of (LDM).

关键词： Laplace Decomposition Method Nonlinear Partial Differential Equations Fifth-Order kdv Equation The Kawahara Equation

EFFECT OF CURRENT ON THE EVOLUTION OF A SOLITARY WAVE

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Science China Mathematics 1985年第12期 1278-1290页

作者：周显初 Beijing Institute of Mechanics Academia Sinica

In this paper, the effect of current on the evolution of a solitary wave is studied. The governing equation in the far field, kdv equation with variable coefficients, is derived. A solitary wave solution is obtained. The fission of a solitary wave is discussed, and the fissible region on the Q～h-plane and the criterion of the number of the solitary waves after fission are found.

关键词： kdv SOL

Exact Traveling Wave Solutions of Nonlinear PDEs in Mathematical Physics

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Applied Mathematics 2012年第7期3卷 738-745页

作者： Jameel F. Alzaidy Mathematics Department Faculty of Science Taif University Kingdom of Saudi Arabia

In the present article, we construct the exact traveling wave solutions of nonlinear PDEs in mathematical physics via the variant Boussinesq equations and the coupled kdv equations by using the extended mapping method and auxiliary equation method. This method is more powerful and will be used in further works to establish more entirely new solutions for other kinds of nonlinear partial differential equations arising in mathematical physics.

关键词： Extended Mapping Method Auxiliary Equation Method The Variant Boussinesq Equations The Coupled kdv Equations Traveling Wave Solutions