Results 21 to 30 of about 5,295 (178)
Soliton interaction with external forcing within the Korteweg–de Vries equation [PDF]
, 2019 We revise the solutions of the forced Korteweg–de Vries equation describing a resonant interaction of a solitary wave with external pulse-type perturbations.
Yury Stepanyants +3 more
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Results in Physics, 2021 This paper is devoted to addressings the fairly interesting soliton solutions for the time fractional combined Korteweg-de Vries-modified Korteweg-de Vries equation (KdV–mKdV equation) and modified Burgers-KdV equation.
Muhammad Naveed Rafiq +5 more
doaj +1 more source
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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Solving nonlinear PDEs using the higher order Haar wavelet method on nonuniform and adaptive grids
Mathematical Modelling and Analysis, 2021 The higher order Haar wavelet method (HOHWM) is used with a nonuniform grid to solve nonlinear partial differential equations numerically. The Burgers’ equation, the Korteweg–de Vries equation, the modified Korteweg–de Vries equation and the sine–Gordon ...
Mart Ratas, Andrus Salupere, Jüri Majak
doaj +1 more source
On Integration of the Loaded mKdV Equation in the Class of Rapidly Decreasing Functions
Известия Иркутского государственного университета: Серия "Математика", 2021 The paper is devoted to the integration of the loaded modified Kortewegde Vries equation in the class of rapidly decreasing functions. It is well known that loaded differential equations in the literature are usually called equations containing in the ...
A.B. Khasanov, U. A. Hoitmetov
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On the discrete and continuous Miura chain associated with the sixth Painlev equation [PDF]
, 2000 A Miura chain is a (closed) sequence of differential (or difference) equations that are related by Miura or B\"acklund transformations. We describe such a chain for the sixth Painlev\'e equation (\pvi), containing, apart from \pvi itself, a Schwarzian ...
Hone, A. N. W. +8 more
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Mathematics, 2022 This paper covers the construction and research of a scheme to solve the problem with nonlinear dispersion wave equations, described by the model Korteweg–de Vries equation.
Alexander Sukhinov +4 more
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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
doaj
Nonlinear Engineering, 2023 In this work, the generalized scale-invariant analog of the Korteweg–de Vries equation is studied. For the first time, the tanh–coth methodology is used to find traveling wave solutions for this nonlinear equation.
González-Gaxiola Oswaldo +1 more
doaj +1 more source
An initial-boundary value problem for the Korteweg-de Vries equation on the negative quarter-plane
, 2009 For the abstract of this paper, please see the PDF ...
Leach, John, Leach, JA, Shaw, S
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