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Abundant different types of soliton solutions for fractional modified KdV equation using auxiliary equation method [PDF]
Scientific ReportsThis research focuses on investigating soliton solutions for the space-time fractional modified third-order Korteweg-de Vries equation using the auxiliary equation method. The Korteweg-de Vries equation is renowned for its application in modeling shallow-
Akhtar Hussain +5 more
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Effect of Coriolis constant on Geophysical Korteweg-de Vries equation
Journal of Ocean Engineering and Science, 2019 The present article investigates the effect of Coriolis constant on the solution of the Geophysical Korteweg-de Vries (gKdV) equation. As such, the Homotopy Perturbation Method (HPM) has been applied here for solving the nonlinear gKdV equation.
P. Karunakar, S. Chakraverty
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The Sylvester equation and the elliptic Korteweg-de Vries system [PDF]
Journal of Mathematical Physics, 2017 The elliptic potential Korteweg-de Vries lattice system is a multi-component extension of the lattice potential Korteweg-de Vries equation, whose soliton solutions are associated with an elliptic Cauchy kernel (i.e., a Cauchy kernel on the torus).
Da-jun Zhang, Frank Nijhoff
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Higher-order Korteweg-de Vries models for internal solitary waves in a stratified shear flow with a free surface [PDF]
Nonlinear Processes in Geophysics, 2002 A higher-order extension of the familiar Korteweg-de Vries equation is derived for internal solitary waves in a density- and current-stratified shear flow with a free surface. All coefficients of this extended Korteweg-de Vries equation are expressed
R. Grimshaw +2 more
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Weak damping for the Korteweg-de Vries equation
Electronic Journal of Qualitative Theory of Differential Equations, 2021 For more than 20 years, the Korteweg–de Vries equation has been intensively explored from the mathematical point of view. Regarding control theory, when adding an internal force term in this equation, it is well known that the Korteweg–de Vries equation ...
Roberto de A. Capistrano Filho
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Open Mathematics, 2022 In this paper, we study the initial boundary problem of fifth-order Korteweg-de Vries equation with nonlinear boundary values. First, we establish a so-called sharp boundary trace regularity associated with the linearized fifth-order Korteweg-de Vries ...
Zhao Xiangqing +2 more
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Results in Physics, 2023 This article mainly studies the new traveling wave solutions of the stochastic modified Korteweg–de Vries equation with multiplicative noise. The traveling wave solutions in the form of hyperbolic function, trigonometric function, rational function and ...
Da Shi, Zhao Li, Tianyong Han
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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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Dynamics investigation of (1+1)-dimensional time-fractional potential Korteweg-de Vries equation
Alexandria Engineering Journal, 2022 The potential Korteweg-de Vries equation arises in the study of water waves and is reported in the dynamics of tsunami waves. The fractional order potential Korteweg-de Vries equation is more flexible and generalized than its classical form. In this work,
Ghazala Akram +3 more
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The discrete Korteweg-de Vries equation [PDF]
Acta Applicandae Mathematicae, 1995 The lattice version of the KdV equation studied in this paper is \[ (p - q + u_{n, m + 1} - u_{n + 1, m}) (p + q - u_{n + 1, m + 1} + u_{n, m}) = p^2 - q^2, \] where \(p,q \in \mathbb{C}\) are lattice parameters. The discretization has been done both in space and time. This equation was derived and studied in a series of previous papers.
Nijhoff, F.W., Capel, H.W.
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