Results 11 to 20 of about 59,702,858 (214)
Convergence of the Rosenau-Korteweg-de Vries Equation to the Korteweg-de Vries One [PDF]
Contemporary Mathematics, 2020 The Rosenau-Korteweg-de Vries equation describes the wave-wave and wave-wall interactions. In this paper, we prove that, as the diffusion parameter is near zero, it coincides with the Korteweg-de Vries equation. The proof relies on deriving suitable a priori estimates together with an application of the Aubin-Lions Lemma.
Coclite, Giuseppe Maria +1 more
openaire +3 more sources
The Extended Korteweg-de Vries Equation [PDF]
Zeitschrift für Naturforschung A, 1982 A slight and natural extension of the traditional Korteweg-de Vries equation (KdV) allows all (or groups) of its solitons to have the same velocity thus facilitating the application of the KdV to realistic quantum mechanical problems.
Hefter, E.F.
openaire +4 more sources
On the Stochastic Korteweg–de Vries Equation [PDF]
Journal of Functional Analysis, 1998 The authors study the following stochastic partial differential equation \[ {\partial u\over \partial t}+ {\partial^3 u\over\partial x^3} +u{\partial u\over \partial x} =f+ \Phi(u) {\partial^2 B\over \partial t\partial x}, \tag{*} \] where \(u\) is a random process defined on \((x,t)\in \mathbb{R}\times \mathbb{R}^+\), \(f\) is a deterministic forcing ...
de Bouard, A, Debussche, A
openaire +3 more sources
Results in Applied MathematicsIn this paper we investigate the fractional modified Korteweg de Vries-sine-Gordon equation and show the inverse scattering transform method can also be used to obtain soliton solutions of fractional modified Korteweg de Vries-sine-Gordon equation. It is
Bazar Babajanov, Fakhriddin Abdikarimov
doaj +2 more sources
Informatika, 2017 The results of computer simulation N-soliton solutions of the Korteweg – de Vries equation with N = 1, 2, 3, 4 are shown. Using numerical experiment the property of conservation of area under the envelope of soliton solutions of the Korteweg – de Vries ...
Y. F. Novik
doaj +1 more source
Lagrangian structures and multidimensional consistency [PDF]
, 2010 The conventional point of view is that the Lagrangian is a scalar object (or equivalently a volume form), which through the Euler-Lagrange equations provides us with one single equation (i.e., one per component of the dependent variable ...
Lobb, Sarah Beverley
core +6 more sources
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
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
On the Korteweg‐de Vries equation: an associated equation [PDF]
International Journal of Mathematics and Mathematical Sciences, 1984 The purpose of this paper is to describe a relationship between the Korteweg‐de Vries (KdV) equation urn:x-wiley:01611712:media:ijmm237357:ijmm237357-math-0001 and another nonlinear partial differential equation of the form urn:x-wiley:01611712:media:ijmm237357:ijmm237357-math-0002 The second equation will be called the Associated Equation (AE ...
Eugene P. Schlereth, Ervin Y. Rodin
openaire +2 more sources
The d-bar formalism for the modified Veselov-Novikov equation on the half-plane [PDF]
Opuscula Mathematica, 2022 We study the modified Veselov-Novikov equation (mVN) posed on the half-plane via the Fokas method, considered as an extension of the inverse scattering transform for boundary value problems.
Guenbo Hwang, Byungsoo Moon
doaj +1 more source