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Numerical solution of the Korteweg-de Vries (KdV) equation
Chaos, Solitons & Fractals, 1997zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jain, P. C. +2 more
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Scattering theory for the Korteweg-De Vries (KdV) equation and its Hamiltonian interpretation
Physica D: Nonlinear Phenomena, 1986The paper deals with the Korteweg-de Vries equation of the form \(u_ t- 6uu_ x+u_{xxx}=0\) and shows that the scattering transform for it is not canonical in the naive sense as it produces ''paradoxes'', one of which is also presented. An explanation of this phenomenon is found, a correct Hamiltonian formulation of the scattering theory is proposed. It
Buslaev, V. S. +2 more
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International Journal of Geometric Methods in Modern Physics, 2021
In this work, we develop a novel method to obtain numerical solution of well-known Korteweg–de Vries (KdV) equation. In the novel method, we generate differentiation matrices for spatial derivatives of the KdV equation by using delta-shaped basis functions (DBFs). For temporal integration we use a high order geometric numerical integrator based on Lie
Polat, Murat, Oruç, Ömer
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In this work, we develop a novel method to obtain numerical solution of well-known Korteweg–de Vries (KdV) equation. In the novel method, we generate differentiation matrices for spatial derivatives of the KdV equation by using delta-shaped basis functions (DBFs). For temporal integration we use a high order geometric numerical integrator based on Lie
Polat, Murat, Oruç, Ömer
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The Korteweg-de Vries Equation (KdV-Equation)
1981This is the classic example of an equation which exhibits solitons. Methods which are applicable to a large class of equations which exhibit solitons will be derived from the study of this equation and its properties, and we therefore devote a rather large part of this book to this topic.
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The Korteweg–de Vries (KdV) Equation
Abstract In this chapter we study the quintessential model for propagation of surface waves in a nonlinear medium: the Korteweg-de Vries (KdV) equation. Its wide applicability stems from the fact that the KdV is a prototypical (normal form) partial differential equation (PDE) that supports nonlinear waves.R. Carretero-González +2 more
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Physics Letters A, 1974
Abstract The non-linear Miura transformation, which converts the N -soliton solution of the modified KdV equation into an N -soliton solution for the KdV equation itself, is related to an unitary transformation of the operators associated with these equations.
T.L. Perelman +2 more
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Abstract The non-linear Miura transformation, which converts the N -soliton solution of the modified KdV equation into an N -soliton solution for the KdV equation itself, is related to an unitary transformation of the operators associated with these equations.
T.L. Perelman +2 more
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Applied Mechanics and Materials, 2012
It is difficult to obtain exact solutions of the nonlinear partial differential equations (PDEs) due to the complexity and nonlinearity, especially for non-integrable systems. In this case, some reasonable approximations of real physics are considered, by means of the standard truncated expansion approach to solve real nonlinear system is proposed.
Jiang Long Wu, Wei Rong Yang
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It is difficult to obtain exact solutions of the nonlinear partial differential equations (PDEs) due to the complexity and nonlinearity, especially for non-integrable systems. In this case, some reasonable approximations of real physics are considered, by means of the standard truncated expansion approach to solve real nonlinear system is proposed.
Jiang Long Wu, Wei Rong Yang
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The European Physical Journal B, 2006
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Wei, Guang-Mei +3 more
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Wei, Guang-Mei +3 more
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2019
Some recent results concerning nonlinear non-Abelian KdV and mKdV equations are presented. Operator equations are studied in references [2]-[7] where structural properties of KdV type equations are investigated. Now, in particular, on the basis of results, the special finite dimensional case of matrix soliton equations is addressed to: solutions of ...
Sandra Carillo +2 more
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Some recent results concerning nonlinear non-Abelian KdV and mKdV equations are presented. Operator equations are studied in references [2]-[7] where structural properties of KdV type equations are investigated. Now, in particular, on the basis of results, the special finite dimensional case of matrix soliton equations is addressed to: solutions of ...
Sandra Carillo +2 more
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Mathematical Notes, 1994
We consider the following system of nonlinear evolution equations: \[ \begin{aligned} \dot b_n & = b_n\Biggl(c_1(b_{n+ 1}- b_{n- 1})- c_2\Biggl(b_{n+ 1} \Biggl(\sum^2_{k= 0} b_{n+ k}\Biggr)- b_{n- 1} \Biggl(\sum^2_{k= 0} b_{n+ k}\Biggr)\Biggr)\Biggr),\tag{1}\\ b_n & = b_n(t),\quad t\in [0, T),\quad n\in \mathbb{Z};\quad c_1, c_2\in \mathbb{C};\;\cdot =
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We consider the following system of nonlinear evolution equations: \[ \begin{aligned} \dot b_n & = b_n\Biggl(c_1(b_{n+ 1}- b_{n- 1})- c_2\Biggl(b_{n+ 1} \Biggl(\sum^2_{k= 0} b_{n+ k}\Biggr)- b_{n- 1} \Biggl(\sum^2_{k= 0} b_{n+ k}\Biggr)\Biggr)\Biggr),\tag{1}\\ b_n & = b_n(t),\quad t\in [0, T),\quad n\in \mathbb{Z};\quad c_1, c_2\in \mathbb{C};\;\cdot =
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