Results 81 to 90 of about 453 (182)
Using Crank-Nikolson Scheme to Solve the Korteweg-de Vries (KdV) Equation
CoRRThe 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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Alexandria Engineering JournalThis work introduces two (3+1)-dimensional expansions of the Korteweg–de Vries (KdV) and modified KdV (mKdV) equations. These extensions incorporate a second-order time-derivative term, similar to the Boussinesq equation. The Painlevé test is utilized to
Abdul-Majid Wazwaz +3 more
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Lax representation with first-order operators for new nonlinear Korteweg – de Vries type equations
Известия высших учебных заведений. Поволжский регион: Физико-математические науки, 2022 Background. In this work, a new representation is constructed for equations of the Korteweg – de Vries (KdV) type. The proposed approach allows to obtain a universal Lax representation for a set of nonlinear partial differential equations, for which ...
V.M. Zhuravlev, V.M. Morozov
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Shallow water cnoidal wave interactions [PDF]
Nonlinear Processes in Geophysics, 1994 The nonlinear dynamics of cnoidal waves, within the context of the general N-cnoidal wave solutions of the periodic Korteweg-de Vries (KdV) and Kadomtsev-Petvishvilli (KP) equations, are considered.
A. R. Osborne
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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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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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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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Unique continuation principle for high order equations of Korteweg-de Vries type
Electronic Journal of Differential Equations, 2013 In this article we consider the problem of unique continuation for high-order equations of Korteweg-de Vries type which include the kdV hierarchy.
Pedro Isaza
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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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