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Analytical and Numerical Computations of Multi-Solitons in the Korteweg-de Vries (KdV) Equation [PDF]
Applied Mathematics, 2020 In this paper, an analytical and numerical computation of multi-solitons in Korteweg-de Vries (KdV) equation is presented. The KdV equation, which is classic of all model equations of nonlinear waves in the soliton phenomena, is described. In the analytical computation, the multi-solitons in KdV equation are computed symbolically using computer ...
Hycienth O. Orapine +2 more
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Electronic Journal of Applied Mathematics, 2023 New solitary wave solutions for the Korteweg-de Vries (KdV) equation by a new version of the trial equation method are attained. Proper transformation reduces the Korteweg-de Vries (KdV) equation to a quadratic ordinary differential equation that is fully integrated using the new version trial equation approach. The family of solitary wave solutions of
Pandir, Yusuf, Ekin, Ali
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Second Order Scheme For Korteweg-De Vries (KDV) Equation
Journal of Bangladesh Academy of Sciences, 2019 The kinematics of the solitary waves is formed by Korteweg-de Vries (KdV) equation. In this paper, a third order general form of the KdV equation with convection and dispersion terms is considered. Explicit finite difference schemes for the numerical solution of the KdV equation is investigated and stability condition for a first-order scheme using ...
Laek Sazzad Andallah +1 more
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BOUNDARY CONTROLLABILITY FOR THE TIME-FRACTIONAL NONLINEAR KORTEWEG-DE VRIES (KDV) EQUATION
Journal of Applied Analysis & Computation, 2020 Recently, time-fractional PDE has received much attention due to its advantages in modeling complex systems. It allows us to tackle efficiently problems involving complexity, self-similar, scale-free, and inverse power law. In particular, time-fractional PDE provides an excellent way for the description of memory and hereditary properties of various ...
Wang, Jingqun, Tian, Lixin
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Wavelet-based Numerical Approaches for Solving the Korteweg-de Vries (KdV) Equation
Turkish Journal of Mathematics and Computer Science, 2022 In this research work, we examine the Korteweg-de Vries equation (KdV), which is utilized to formulate the propagation of water waves and occurs in different fields such as hydrodynamics waves in cold plasma acoustic waves in harmonic crystals. This research presents two efficient computational methods based on Legendre wavelets to solve the Korteweg ...
Neslihan ÖZDEMİR, Aydın SEÇER
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Structure-Preserving Physics-Informed Neural Network for the Korteweg--de Vries (KdV) Equation [PDF]
Physics-Informed Neural Networks (PINNs) offer a flexible framework for solving nonlinear partial differential equations (PDEs), yet conventional implementations often fail to preserve key physical invariants during long-term integration. This paper introduces a \emph{structure-preserving PINN} framework for the nonlinear Korteweg--de Vries (KdV ...
Obieke, Victory, Oguadimma, Emmanuel
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Non-central m-point formula in method of lines for solving the Korteweg-de Vries (KdV) equation [PDF]
Journal of Umm Al-Qura University for Applied SciencesAbstract The present study is committed to devising efficient spatial discretization with two non-central difference formulae incorporated in the method of lines (MOL). The method is then implemented numerically on the renowned dispersive evolution equation, the Korteweg-de Vries (KdV) model while infusing Euler and fourth-order Rung-Kutta ...
A. Alshareef, H. O. Bakodah
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An extension of the steepest descent method for Riemann-Hilbert problems: The small dispersion limit of the Korteweg-de Vries (KdV) equation [PDF]
Proceedings of the National Academy of Sciences, 1998 This paper extends the steepest descent method for Riemann-Hilbert problems introduced by Deift and Zhou in a critical new way. We present, in particular, an algorithm, to obtain the support of the Riemann-Hilbert problem for leading asymptotics. Applying this extended method to small dispersion KdV (Korteweg-de Vries) equation, we (
Deift, P., Venakides, S., Zhou, X.
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Using Crank-Nikolson Scheme to Solve the Korteweg-de Vries (KdV) Equation [PDF]
The Korteweg-de Vries (KdV) equation is a fundamental partial differential equation that models wave propagation in shallow water and other dispersive media. Accurately solving the KdV equation is essential for understanding wave dynamics in physics and engineering applications.
Qiming Wu
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Weakly nonlinear wavepackets in the Korteweg–de Vries equation: the KdV/NLS connection [PDF]
Mathematics and Computers in Simulation, 2001 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Boyd, John P., Chen, Guan-Yu
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