On the generalized korteweg-de vries equation

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Web28 de dez. de 2001 · 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 ... Web11 de abr. de 2024 · The focus here is upon the generalized Korteweg–de Vries equation, \begin {aligned} u_t + u_x + \frac {1} {p} \left ( u^p \right) _x +u_ {xxx} \, = \, 0, \end …

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Web1 de mai. de 1990 · Abstract. We study the longtime stability of small solutions to the IVP for the generalized Korteweg-de Vries equation. We obtain a lower bound for the degrees of nonlinearity of the perturbation which guarantees that the small solutions of the nonlinear problem behave asymptotically like the solutions of the associated linear problem. Web1 de set. de 2006 · We consider the local and global Cauchy problem for the generalized Korteweg-de Vries equation, with initial data in homogeneous and nonhomogeneous Besov spaces. This allows us to slightly extend known results on this problem. Furthermore we prove existence and uniqueness of self-similar solutions. pondwicks amersham

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WebWe show well-posedness results for the generalized Korteweg-de Vries equation with nonlinear term F (u)∂xu F ( u) ∂ x u. We assume F (u) F ( u) is a C4 C 4 function and F … WebS. Oh, Resonant phase-shift and global smoothing of the periodic Korteweg–de Vries equation in low regularity settings, Adv. Differential Eq. 18(7–8) (2013) 633–662. Google Scholar; 30. J. Shatah, Normal forms and quadratic nonlinear Klein–Gordon equations, Comm. Pure Appl. Math. 38 (1985) 685–696. Crossref, ISI, Google Scholar; 31. V. shanty river tubes

Two remarks on the generalised Korteweg de-Vries equation

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Web在这篇论文，我们把我们的焦点放在一个可变系数的第五顺序的 Korteweg-de Vries (fKdV ) 方程上，它拥有很多优秀性质并且具有物理、工程的领域里的当前的重要性。某些限制被得出，它确认如此的一个方程的 integrability。在那些限制下面，一些 integrable 性质被导出，例如宽松的对和 Darboux 转变。经由 ... Web15 de ago. de 1991 · KORTEWEG-DE VRIES EQUATION 97 4. PROOF OF THEOREM 1 (A) The point of departure is the integral equation (see also (1.10)) u (t}=S (t)g+ [' S (t … pondwicks close st albansWebWith the inhomogeneities of media taken into account, under investigation is hereby a generalized variable-coefficient forced Korteweg-de Vries (vc-fKdV) equation, which … pond wheat grass

"Web4 de nov. de 2006 · Then passing to the limit in this sequence, we get the persistence for the solution u (t) in X 2,θ as desired. Moreover, since X s,1 ⊆ X s,θ , for all s ∈ R and θ ∈ [0] [1], see Remark 1. ... " - On the generalized korteweg-de vries equation

On the generalized korteweg-de vries equation

On the Korteweg-de Vries equation - Springer

Web5 de nov. de 1996 · Recent numerical simulations of the generalized Korteweg—de Vries equation u t + u p u x + u xxx = 0 indicate that for p⩾4, smooth solutions of the initial-value problem may form singularities in finite time. It is the purpose of this paper to ascertain what effect dissipation has on the instability of solitary waves and the associated blow-up … WebIn the last twenty years, there have been significant advances in the study of the blow-up phenomenon for the critical generalized Korteweg-de Vries equation, including the determination of sufficient conditions for blowup, the stability of blowup in a refined topology and the classification of minimal mass blowup. Exotic blow-up solutions with a continuum …

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WebThis paper is concerned with the controllability of the linear Korteweg–de Vries equation on the domain Ω = (0,+∞), the control being applied at the left endpoint x = 0. It is shown that the exact boundary controllability holds true in L2(0,+∞) provided that the solutions are not required to be in L∞(0, T, L2(0,+∞)). Web@article{osti_5711174, title = {On the Korteweg-de Vries equations}, author = {Ramirez, R and Sadovskaia, N and Avis, R L}, abstractNote = {The modern focus of Hamiltonian formalism takes as a fundamental aspect of its approach the Poisson bracket. Let C{sup {infinity}}(M) be the ring of all infinitely differentiable functions in a certain manifold M.

WebExistence, uniqueness, and continuous dependence on the initial data are proved for the local (in time) solution of the (generalized) Korteweg-de Vries equation on the real line, … Web28 de fev. de 1984 · GENERALIZED SOLUTIONS OF THE CAUCHY PROBLEM FOR THE KORTEWEG-DE VRIES EQUATION. Mathematics of the USSR-Sbornik , Volume 48 , Number 2 Citation S N Kruzhkov and A V Faminskiĭ 1984 Math. USSR Sb. 48 391 DOI 10.1070/SM1984v048n02ABEH002682.

Web15 de abr. de 1995 · Hasan A and Foss B (2011) Global Stabilization of The Generalized Burgers-Korteweg-de Vries Equation by Boundary Control, IFAC Proceedings … Webthe (slightly generalized) KdV equation (i.i) u t § Uxx x + a(u)u x = 0, t ~ 0, -= < x < =, (1.2) u(0,x) = g(x). Here all functions are real-valued, and a is assumed to be C ~ (though we …

Web7 de fev. de 2007 · 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.

WebDecember 1989 On the (generalized) Korteweg-de Vries equation Carlos E. Kenig , Gustavo Ponce , Luis Vega Duke Math. J. 59(3): 585-610 (December 1989). shanty restaurant wisconsinWeb31 de dez. de 2010 · Numerical Study of breakup in generalized Korteweg-de Vries and Kawahara equations. B. Dubrovin, T. Grava, C. Klein. This article is concerned with a … shanty restaurant in wadsworth illinoisWebA note on the quartic generalized Korteweg-de Vries equation in weighted Sobolev spaces . × Close Log In. Log in with Facebook Log in with Google. or. Email. Password. Remember me on this computer. or reset password. Enter the email address you signed up with and we'll email you a reset ... pond wineryWebThe generalized Korteweg-de Vries equation (KdV) is given by where p is a positive parameter. Formulated in the moving frame ξ = x - ct, the generalized Korteweg-de … shanty rockerWebProceedings of the American Mathematical Society. Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics. ISSN 1088-6826 (online) ISSN 0002-9939 (print) shanty restaurant wadsworth ilWebKorteweg–De Vries equation. Cnoidal wave solution to the Korteweg–De Vries equation, in terms of the square of the Jacobi elliptic function cn (and with value of the parameter … shanty rhode islandWebThis paper proposes a new class of arbitrarily high-order conservative numerical schemes for the generalized Korteweg--de Vries (KdV) equation. This approach is based on the scalar auxiliary variable method. The equation is reformulated into an equivalent system by introducing a scalar auxiliary variable, and the energy is reformulated into a sum of two … shanty river tubing