Numerical investigation for solitary solutions of the Boussinesq equation.
Al-Khaled, Kamel, Nusier, Ameina S. (2008)
Applied Mathematics E-Notes [electronic only]
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Displaying similar documents to “Analytical and numerical methods for the CMKdV-II equation.”
Numerical investigation for solitary solutions of the Boussinesq equation.
Numerical comparisons of two long-wave limit models
Stéphane Labbé, Lionel Paumond (2004)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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The Benney-Luke equation (BL) is a model for the evolution of three-dimensional weakly nonlinear, long water waves of small amplitude. In this paper we propose a nearly conservative scheme for the numerical resolution of (BL). Moreover, it is known (Paumond, Differential Integral Equations 16 (2003) 1039–1064; Pego and Quintero, Physica D 132 (1999) 476–496) that (BL) is linked to the Kadomtsev-Petviashvili equation for almost one-dimensional waves propagating in one direction. We study...
Solitary-wave propagation and interactions for a sixth-order generalized Boussinesq equation.
Feng, Bao-Feng, Kawahara, Takuji, Mitsui, Taketomo, Chan, Youn-Sha (2005)
International Journal of Mathematics and Mathematical Sciences
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Higher-order equations of the KdV type are integrable.
Marinakis, V. (2010)
Advances in Mathematical Physics
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New exact traveling wave solutions of the ()-dimensional Zakharov-Kuznetsov (ZK) equation.
Khalfallah, Mohammed (2007)
Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică
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Approximate method for studying the waves propagating along the interface between air-water.
Khader, M.M., Al-Bar, R.F. (2011)
Mathematical Problems in Engineering
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Convergence of Fourier spectral method for resonant long-short nonlinear wave interaction
Abdur Rashid, Shakaib Akram (2010)
Applications of Mathematics
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In this paper, the evolution equations with nonlinear term describing the resonance interaction between the long wave and the short wave are studied. The semi-discrete and fully discrete Crank-Nicholson Fourier spectral schemes are given. An energy estimation method is used to obtain error estimates for the approximate solutions. The numerical results obtained are compared with exact solution and found to be in good agreement.
On the Korteweg-de Vries equation: an associated equation.
Schlereth, Eugene P., Rodin, Ervin Y. (1984)
International Journal of Mathematics and Mathematical Sciences
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New exact traveling wave solutions for compound KdV-Burgers equations in mathematical physics.
Zheng, Xuedong, Xia, Tiecheng, Zhang, Hongqing (2002)
Applied Mathematics E-Notes [electronic only]
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Programming of the generalized nonlinear paraxial equation for the formation of solitons with Mathematica.
Osman, Frederick, Beech, Robert (2005)
Journal of Applied Mathematics and Decision Sciences
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Computing exact solutions to a generalized Lax-Sawada-Kotera-Itô seventh-order KdV equation.
Salas, Alvaro H., Gómez S, Cesar A., Frias, Bernardo Acevedo (2010)
Mathematical Problems in Engineering
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A finite element method for extended KdV equations
Anna Karczewska, Piotr Rozmej, Maciej Szczeciński, Bartosz Boguniewicz (2016)
International Journal of Applied Mathematics and Computer Science
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The finite element method (FEM) is applied to obtain numerical solutions to a recently derived nonlinear equation for the shallow water wave problem. A weak formulation and the Petrov-Galerkin method are used. It is shown that the FEM gives a reasonable description of the wave dynamics of soliton waves governed by extended KdV equations. Some new results for several cases of bottom shapes are presented. The numerical scheme presented here is suitable for taking into account stochastic...