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Travelling Solitary Wave Solutions to Higher Order Korteweg-de Vries Equation 被引量:3
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作者 Chunhuan Xiang Honglei Wang 《Open Journal of Applied Sciences》 2019年第5期354-360,共7页
The travelling solitary wave solutions to the higher order Korteweg-de Vries equation are obtained by using tanh-polynomial method. The method is effective and concise, which is also applied to various partial differe... The travelling solitary wave solutions to the higher order Korteweg-de Vries equation are obtained by using tanh-polynomial method. The method is effective and concise, which is also applied to various partial differential equations to obtain traveling wave solutions. The numerical simulation of the solutions is given for completeness. Numerical results show that the tanh-polynomial method works quite well. 展开更多
关键词 higher order korteweg-de vries equation TRAVELLING WAVE Solutions SOLITARY WAVE
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Discrete Singular Convolution Method for Numerical Solutions of Fifth Order Korteweg-De Vries Equations 被引量:2
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作者 Edson Pindza Eben Maré 《Journal of Applied Mathematics and Physics》 2013年第7期5-15,共11页
A new computational method for solving the fifth order Korteweg-de Vries (fKdV) equation is proposed. The nonlinear partial differential equation is discretized in space using the discrete singular convolution (DSC) s... A new computational method for solving the fifth order Korteweg-de Vries (fKdV) equation is proposed. The nonlinear partial differential equation is discretized in space using the discrete singular convolution (DSC) scheme and an exponential time integration scheme combined with the best rational approximations based on the Carathéodory-Fejér procedure for time discretization. We check several numerical results of our approach against available analytical solutions. In addition, we computed the conservation laws of the fKdV equation. We find that the DSC approach is a very accurate, efficient and reliable method for solving nonlinear partial differential equations. 展开更多
关键词 FIFTH order korteweg-de vries equations Discrete Singular Convolution Exponential Time Discretization METHOD Soliton Solutions Conservation LAWS
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PainlevéAnalysis of Higher Order Nonlinear Evolution Equations with Variable Coefficients
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作者 Wang Yuan 《Chinese Quarterly Journal of Mathematics》 2021年第2期196-203,共8页
There is a close relationship between the Painlevéintegrability and other integrability of nonlinear evolution equation.By using the Weiss-Tabor-Carnevale(WTC)method and the symbolic computation of Maple,the Pain... There is a close relationship between the Painlevéintegrability and other integrability of nonlinear evolution equation.By using the Weiss-Tabor-Carnevale(WTC)method and the symbolic computation of Maple,the Painlevétest is used for the higher order generalized non-autonomous equation and the third order Korteweg-de Vries equation with variable coefficients.Finally the Painlevéintegrability condition of this equation is gotten. 展开更多
关键词 higher order generalized non-autonomous equation Third order korteweg-de vries equation with variable coefficients Painlevéanalysis method
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A HIGH-ORDER PAD SCHEME FOR KORTEWEG-DE VRIES EQUATIONS 被引量:2
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作者 XU Zhen-li LIU Ru-xun 《Journal of Hydrodynamics》 SCIE EI CSCD 2005年第6期654-659,共6页
A high-order finite difference Pade scheme also called compact scheme for solving Korteweg-de Vries (KdV) equations, which preserve energy and mass conservations, was developed in this paper. This structure-preservi... A high-order finite difference Pade scheme also called compact scheme for solving Korteweg-de Vries (KdV) equations, which preserve energy and mass conservations, was developed in this paper. This structure-preserving algorithm has been widely applied in these years for its advantage of maintaining the inherited properties. For spatial discretization, the authors obtained an implicit compact scheme by which spatial derivative terms may be approximated through combining a few knots. By some numerical examples including propagation of single soliton and interaction of two solitons, the scheme is proved to be effective. 展开更多
关键词 korteweg-de vries (KdV) equation compact finite difference scheme solitory waves high order
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Solitary wave solutions to higher-order traffic flow model with large diffusion
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作者 菅肖霞 张鹏 +2 位作者 S.C.WONG 乔殿梁 崔岐柱 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2014年第2期167-176,共10页
This paper uses the Taylor expansion to seek an approximate Korteweg- de Vries equation (KdV) solution to a higher-order traffic flow model with sufficiently large diffusion. It demonstrates the validity of the appr... This paper uses the Taylor expansion to seek an approximate Korteweg- de Vries equation (KdV) solution to a higher-order traffic flow model with sufficiently large diffusion. It demonstrates the validity of the approximate KdV solution considering all the related parameters to ensure the physical boundedness and the stability of the solution. Moreover, when the viscosity coefficient depends on the density and velocity of the flow, the wave speed of the KdV solution is naturally related to either the first or the second characteristic field. The finite element method is extended to solve the model and examine the stability and accuracy of the approximate KdV solution. 展开更多
关键词 higher-order traffic flow model viscosity coefficient approximate korteweg-de vries equation (KdV) solution finite element scheme
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