Results 101 to 110 of about 8,902 (211)
Traveling Wave Solutions of Space-Time Fractional Generalized Fifth-Order KdV Equation
Advances in Mathematical Physics, 2017 The Korteweg-de Vries (KdV) equation, especially the fractional higher order one, provides a relatively accurate description of motions of long waves in shallow water under gravity and wave propagation in one-dimensional nonlinear lattice.
Dianchen Lu, Chen Yue, Muhammad Arshad
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Nonlinear Engineering, 2017 In this paper, a combined form of the Laplace transform method with the homotopy perturbation method is applied to solve nonlinear fifth order Korteweg de Vries (KdV) equations. The method is known as homotopy perturbation transform method (HPTM).
Sharma Dinkar +2 more
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Bäcklund Transformations for Nonlinear Differential Equations and Systems
Axioms, 2019 In this work, new Bäcklund transformations (BTs) for generalized Liouville equations were obtained. Special cases of Liouville equations with exponential nonlinearity that have a multiplier that depends on the independent variables and first-order ...
Tatyana V. Redkina +4 more
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Structure-Preserving Physics-Informed Neural Network for the Korteweg--de Vries (KdV) Equation
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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Fractional View Analysis System of Korteweg–de Vries Equations Using an Analytical Method
Fractal and FractionalThis study introduces two innovative methods, the new transform iteration method and the residual power series transform method, to solve fractional nonlinear system Korteweg–de Vries (KdV) equations.
Yousef Jawarneh +2 more
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A combined sine-Gordon and modified Korteweg-de Vries hierarchy and its algebro-geometric solutions
, 1997 We derive a zero-curvature formalism for a combined sine-Gordon (sG) and modified Korteweg-de Vries (mKdV) equation which yields a local sGmKdV hierarchy.
Gesztesy, Fritz, Holden, Helge
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Non-central m-point formula in method of lines for solving the Korteweg-de Vries (KdV) equation
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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Nonlinear Evolution Equations of the Soliton Type: Old and New Results
ProceedingsAn overview on the study of nonlinear evolution equations of soliton type is provided. In addition, 5th-order nonlinear evolution equations are shown to be connected to the Caudrey–Dodd–Gibbon–Sawada–Kotera (CDGSK) equation via Bäcklund transformations ...
Sandra Carillo +2 more
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Karadeniz Fen Bilimleri Dergisi, 2019 In this article, some soliton wave solutions of the coupled potential KdV equation have been found using the generalized (G '/ G) - expansion method. For this equation, hyperbolic function solutions, trigonometric function solutions and rational function solutions have been obtained.
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Using Crank-Nikolson Scheme to Solve the Korteweg-de Vries (KdV) Equation
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.
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