Results 201 to 210 of about 22,064 (260)

Scattering theory for the Korteweg-De Vries (KdV) equation and its Hamiltonian interpretation

Physica D: Nonlinear Phenomena, 1986
The 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., Faddeev, L. D., Takhtadzhan, L. A.   +2 more
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A combination of Lie group-based high order geometric integrator and delta-shaped basis functions for solving Korteweg–de Vries (KdV) equation

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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Lie group method for solving generalized Hirota–Satsuma coupled Korteweg–de Vries (KdV) equations

Applied Mathematics and Computation, 2013
Method of Lie group has been applied to study Hirota-Satsuma coupled Korteweg-de Vries (KdV) system of partial differential equations. Lie group method is applied to determine symmetry reductions of the nonlinear partial differential equations. The resulting nonlinear ordinary differential equations are solved analytically and the obtained solutions ...
Mina B. Abd-el-Malek, Amr M. Amin
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The Korteweg-de Vries Equation (KdV-Equation)

1981
This 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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Darboux transformations for supersymmetric korteweg-de vries equations

, 1994
We consider the Darboux type transformations for the spectral problems of supersymmetric KdV systems. The supersymmetric analogies of Darboux and Darboux-Levi transformations are established for the spectral problems of Manin-Radul-Mathieu sKdV and Manin-
Q. P. Liu
semanticscholar   +1 more source

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, D.J. Frantzeskakis, P.G. Kevrekidis   +2 more
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On the relationship between the N-soliton solution of the modified Korteweg-de Vries equation and the KdV equation solution

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, A.Kh. Fridman, M.M. El'Yashevich   +2 more
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On the analytical soliton approximations to fractional forced Korteweg–de Vries equation arising in fluids and plasmas using two novel techniques

Communications in Theoretical Physics
The current investigation examines the fractional forced Korteweg–de Vries (FF-KdV) equation, a critically significant evolution equation in various nonlinear branches of science.
Weaam Alhejaili, E. Az-Zo’bi, Rasool Shah, S. A. El-Tantawy   +3 more
semanticscholar   +1 more source

Approximate Solutions of Generalized Fifth-Order Korteweg-De Vries (KdV) Equation by the Standard Truncated Expansion Method

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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Painlevé analysis, auto-Bäcklund transformation and new analytic solutions for a generalized variable-coefficient Korteweg-de Vries (KdV) equation

The European Physical Journal B, 2006
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wei, Guang-Mei, Gao, Yi-Tian, Hu, Wei, Zhang, Chun-Yi   +3 more
openaire   +2 more sources