On the Korteweg-de Vries equation
نویسندگان
چکیده
منابع مشابه
Korteweg-de Vries Equation in Bounded Domains
where μ, ν are positive constants. This equation, in the case μ = 0, was derived independently by Sivashinsky [1] and Kuramoto [2] with the purpose to model amplitude and phase expansion of pattern formations in different physical situations, for example, in the theory of a flame propagation in turbulent flows of gaseous combustible mixtures, see Sivashinsky [1], and in the theory of turbulence...
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The initial-boundary value problem for the generalized Korteweg-de Vries equation on a half-line is studied by adapting the initial value techniques developed by Kenig, Ponce and Vega and Bourgain to the initial-boundary setting. The approach consists of replacing the initial-boundary problem by a forced initial value problem. The forcing is selected to satisfy the boundary condition by inverti...
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We make two observations concerning the generalised Korteweg de Vries equation ut + uxxx = μ(|u|u)x. Firstly we give a scaling argument that shows, roughly speaking, that any quantitative scattering result for L-critical equation (p = 5) automatically implies an analogous scattering result for the L-critical nonlinear Schrödinger equation iut+uxx = μ|u|4u. Secondly, in the defocusing case μ > 0...
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In this paper, we have studied on the solutions of modied KdV equation andalso on the stability of them. We use the tanh method for this investigationand given solutions are good-behavior. The solution is shock wave and can beused in the physical investigations
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We develop and compare some geometric integrators for the Korteweg-de Vries equation, especially with regard to their robustness for large steps in space and time, ∆x and ∆t, and over long times. A standard, semi-explicit, symplectic finite difference scheme is found to be fast and robust. However, in some parameter regimes such schemes are susceptible to developing small wiggles. At the same i...
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ژورنال
عنوان ژورنال: Proceedings of the Japan Academy, Series A, Mathematical Sciences
سال: 1975
ISSN: 0386-2194
DOI: 10.3792/pja/1195518562