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Classical Solutions for the Generalized Korteweg-de Vries Equation
Axioms, 2023 The Korteweg-de Vries equation models the formation of solitary waves in the context of shallow water in a channel. In our system, f or p=2 and p=3 (Korteweg-de Vries equations (KdV)) and (modified Korteweg-de Vries (mKdV) respectively), these equations ...
Svetlin Georgiev +3 more
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Some finite difference methods for solving linear fractional KdV equation
Frontiers in Applied Mathematics and Statistics, 2023 The time-fractional Korteweg de Vries equation can be viewed as a generalization of the classical KdV equation. The KdV equations can be applied in modeling tsunami propagation, coastal wave dynamics, and oceanic wave interactions.
Appanah Rao Appadu, Abey Sherif Kelil
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Jordan manifolds and dispersionless KdV equations [PDF]
, 2000 Multicomponent KdV-systems are defined in terms of a set of structure constants and, as shown by Svinolupov, if these define a Jordan algebra the corresponding equations may be said to be integrable, at least in the sense of having higher-order ...
I. A. B. Strachan +2 more
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On a Schwarzian PDE associated with the KdV hierarchy [PDF]
, 2000 We present a novel integrable non-autonomous partial differential equation of the Schwarzian type, i.e. invariant under M\"obius transformations, that is related to the Korteweg-de Vries hierarchy.
Hone, A. N. W. +8 more
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Exact Solutions to a Class of Schamel Nonlinear Equations Modeling Dust Ion-acoustic Waves in Plasma [PDF]
Assiut University Journal of Multidisciplinary Scientific Research, 2022 In this paper, we apply the extended Kudryashov method to construct some new exact solitary wave solutions of three important physical models, Schamel-nonlinear Schrödinger (S-NLS) equation, Schamel Korteweg-de Vries (S-KdV) equation, Schamel Korteweg-de
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Observations on the tanh-coth expansion method for finding solutions to nonlinear evolution equations [PDF]
, 2010 The 'tanh-coth expansion method' for finding solitary travelling-wave solutions to nonlinear evolution equations has been used extensively in the literature. It is a natural extension to the basic tanh-function expansion method which was developed in the
Parkes, E.J.
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Exact traveling wave solutions to higher order nonlinear equations
Journal of Ocean Engineering and Science, 2019 The present paper applies the new generalized (G′/G)-expansion method on three non-linear equations including the fifth-order Korteweg-de Vries equation, (3+1)-dimensional Modified KdV-Zakharov-Kuznetsov equation, and (3+1)-dimensional Jimbo-Miwa ...
Md Nur Alam, Xin Li
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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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Ain Shams Engineering Journal, 2018 In this paper, we present a numerical method proficient for solving a system of time–fractional partial differential equations. For this sake, we use spectral collection method based on shifted Chebyshev polynomials in space and finite difference method ...
Basim Albuohimad +2 more
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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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