Results 1 to 10 of about 18,026 (175)
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
doaj +2 more sources
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
doaj +4 more sources
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
doaj +1 more source
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
doaj +1 more source
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
doaj +1 more source
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
doaj +1 more source
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
doaj +1 more source
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.
openaire +3 more sources
Қарағанды университетінің хабаршысы. Математика сериясы, 2021 Partial differential equations of the third order are the basis of mathematical models of many phenomena and processes, such as the phenomenon of energy transfer of hydrolysis of adenosine triphosphate molecules along protein molecules in the form of ...
М.B. Muratbekov, A.O. Suleimbekova
doaj +1 more source
Algebraic traveling waves for the modified Korteweg–de-Vries–Burgers equation
Electronic Journal of Qualitative Theory of Differential Equations, 2020 In this paper we characterize all traveling wave solutions of the Generalized Korteweg–de Vries–Burgers equation. In particular we recover the traveling wave solutions for the well-known Korteweg–de Vries–Burgers equation.
Claudia Valls
doaj +1 more source