Results 31 to 40 of about 59,702,858 (214)
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
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On tau functions associated with linear systems [PDF]
, 2012 \noindent {\bf Abstract} This paper considers the Fredholm determinant $\det (I-\Gamma_x)$ of a Hankel integral operator on $L^2(0, \infty )$ with kernel $\phi (s+t+2x)$, where $\phi$ is a matrix scattering function.
Samantha L. Newsham +3 more
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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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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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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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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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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
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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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Asymptotic stability of a Korteweg–de Vries equation with a two-dimensional center manifold
Advances in Nonlinear Analysis, 2018 Local asymptotic stability analysis is conducted for an initial-boundary-value problem of a Korteweg–de Vries equation posed on a finite interval [0,2π7/3]{[0,2\pi\sqrt{7/3}]}.
Tang Shuxia +3 more
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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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