On the generalized korteweg-de vries equation

WebThis 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 … WebThe Korteweg–de Vries equation \\[ u_t + uu_x + u_{xxx} = 0\\] is a nonlinear partial differential equation arising in the study of a number of different physical systems, e.g., …

Nonlinear small data scattering for the generalized Korteweg-de Vries ...

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. WebWe show for the Korteweg-de Vries equation an existence uniqueness theorem in Sobolev spaces of arbitrary fractional order s ≧2, provided the initial data is given in the … eado loft apartments https://gravitasoil.com

Dispersive Equations and Nonlinear Waves: Generalized Korteweg …

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 … WebProceedings 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) 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. ea dodgeball

Nonlinear small data scattering for the generalized Korteweg-de Vries ...

Category:The Korteweg-de Vries Equation: History, exact Solutions, and …

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On the generalized korteweg-de vries equation

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WebIn this letter, we propose a hierarchy of new generalized Korteweg–de Vries equations and find that the generalized Korteweg–de Vries equation has a class of pseudo-peakons. The so-called pseudo-peakon looks like a peakon, but it is continuously differentiable everywhere and its second-order derivative goes to infinity at some point. WebMany physical phenomena in fields of studies such as optical fibre, solid-state physics, quantum field theory and so on are represented using nonlinear evolution equations …

On the generalized korteweg-de vries equation

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Web7 de abr. de 2024 · Find many great new & used options and get the best deals for Dispersive Equations and Nonlinear Waves: Generalized Korteweg-de Vries, at the best online prices at eBay! Dispersive Equations and Nonlinear Waves: Generalized Korteweg-de Vries, 9783034807357 eBay 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. ...

Web25 de nov. de 2024 · The non-linear time-fractional Korteweg-de Vries and modified Korteweg-de Vries equations are studied with Caputo's fractional derivative. The general ... the higher-order localized waves for the coupled mixed derivative nonlinear Schrödinger equation are investigated using generalized Darboux transformation. On the basis of seed 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 ...

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 … 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.

Web24 de jul. de 2006 · DOI: 10.1016/J.PHYSLETA.2006.03.080 Corpus ID: 120358134; Transformations for a generalized variable-coefficient Korteweg de Vries model from blood vessels, Bose Einstein condensates, rods and positons with symbolic computation

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, … csharp photographyWebA 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 ... ead online formWeb11 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 … ead numbersWebAbstract The time-fractional coupled Korteweg–de Vries equations (TFCKdVEs) describe various interesting real-world phenomena including wave propagation and the description of shallow water waves o... c sharp pauseWebIn this paper, we study the orbital stability for a four-parameter family of periodic stationary traveling wave solutions to the generalized Korteweg-de Vries (gKdV) equation csharp pl3WebOn the generalized Korteweg-de Vries equation, Differential Integral Equations 10 (1997), 777–796. Google Scholar Strauss, W. A.: Dispersion of low-energy waves for two … c sharp phrygianWebAbstract The time-fractional coupled Korteweg–de Vries equations (TFCKdVEs) describe various interesting real-world phenomena including wave propagation and the … csharp pid