Results 171 to 180 of about 8,881 (223)
A study of traveling wave solutions and modulation instability in the (3+1)-dimensional Sakovich equation employing advanced analytical techniques. [PDF]
Sci RepAhmad J +5 more
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Multi-type solitary wave solutions of Korteweg–de Vries (KdV) equation
International Journal of Modern Physics B, 2023 In this paper, we explore how to generate solitary, peakon, periodic, cuspon and kink wave solution of the well-known partial differential equation Korteweg–de Vries (KdV) by using exp-function and modified exp-function methods. The presented methods construct more efficiently almost all types of soliton solution of KdV equation that can be rarely ...
Asif Waheed +5 more
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Numerical solution of the Korteweg-de Vries (KdV) equation
Chaos, Solitons & Fractals, 1997 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jain, P. C. +2 more
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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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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. +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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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.
Gert Eilenberger
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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 =
Andrey Osipov
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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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