Breakdown of the camassa-holm equation
WebThis is the “steepening lemma” of Camassa and Holm [2]. Nothing worse happens: v(t, x) itself cannot jump like the usual kind of shock. Actually, it is not the obvious v but rather … WebIn this paper, a difference scheme satisfying two conservative laws for the periodic Camassa-Holm equation is given. Convergence is proved. The numerical simulation exhibits the time evolution and the interaction of solitary wave solutions. ... McKean, H.P.: Breakdown of the Camassa-Holm equation. Comm. Pure Appl. Math. LVII (2004) 416 …
Breakdown of the camassa-holm equation
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WebJun 9, 2024 · A famous feature of the Camassa–Holm equation is its admission of peaked soliton solutions known as peakons. We investigate this equation under the influence of … WebF. Linares, G. Ponce, and T. Sideris, Properties of solutions to the Camassa-Holm equation on the line in a class containing the peakons, Advanced Studies in Pure …
WebDec 2, 2011 · Let us recall that the Cauchy problem associated with Equation () is locally well-posed (in the sense of Hadamard) in for .See, for example, [10, 11] (see also [] for … WebJun 4, 2013 · Recently, much attention has been paid to a class of nonlinear wave equations, which contain the Camassa-Holm (CH) equation, the Degasperis-Procesi …
WebJan 11, 2012 · This paper gives a new and direct proof for McKean’s theorem (McKean in Asian J. Math. 2:867–874, 1998) on wave breaking of the Camassa–Holm equation. The blow-up profile is also analyzed. Download to read the full article text. Bressan, A., Constantin, A.: Global conservative solutions of the Camassa–Holm equation. Arch. WebMar 1, 2002 · 1. Introduction. Camassa and Holm [3] recently gave a dispersive shallow water equation (1) u t +2ku x −u xxt +3uu x =2u x u xx +uu xxx, which is called the CH equation. In the case of k =0, they showed that the solitary wave solution of Eq. (1) is (2) u (x,t)=c e − x−ct , which were named “peakons” to single them out of general ...
WebThe technique is similar to that of McKean, who proved the same for the Camassa–Holm equation, but we introduce a new perspective involving a change of variables to treat the …
WebMay 21, 2024 · The Camassa–Holm equation and its two-component Camassa–Holm system generalization both experience wave breaking in finite time. To analyze this, and to obtain solutions past wave breaking, it ... oxford test psiWebWhile (1.1) is also called the Euler-Poincar´e equations in the higher dimensional case d ≥ 1. In particular, when d = 1,the system (1.1) isthe classical Camassa-Holm (CH) equation, like the KdV equation, the CH equation describes the unidirectional propagation of waves at the free surface of shallow water under the influence of gravity [4 ... oxford texas snow tubingWebJul 2, 2024 · With the aid of reciprocal transformation and the associated modified Camassa–Holm equation, a Bäcklund transformation, which involves both dependent … jeff tiedrich bioWebMar 7, 2024 · Using a generalized framework that consists of evolution of the solution to the Camassa- Holm equation and its energy measure, we establish the global-in-time orbital stability of peakons with respect to the perturbed (energy) conservative solutions to the Camassa-Holm equation. Especially, we extend the H1-stability result obtained by … oxford test of english practice pack b2WebMar 1, 2004 · Breakdown of the Camassa‐Holm equation @article{McKean2004BreakdownOT, title={Breakdown of the Camassa‐Holm … jeff ticknor bmoWebFeb 3, 2012 · Abstract: We exhibit a sufficient condition in terms of decay at infinity of the initial data for the finite time blowup of strong solutions to the Camassa--Holm equation: … jeff tiedrich grateful deadWebDec 1, 2024 · Using a generalized framework that consists of evolution of the solution to the Camassa–Holm equation and its energy measure, we establish the global-in-time orbital stability of peakons with respect to the perturbed (energy) conservative solutions to the Camassa–Holm equation. oxford text cefr checker