On whitham equations for camassa-holm
Web5 de nov. de 2024 · More specifically, we will now focus on the Cauchy problem for the periodic higher-order Camassa–Holm equations, i.e.(1.3){mt+(u2−ux2)p−1uxm+(u(u2−ux2)p−1m)x=0,t>0,x∈S,u(0,x)=u0(x),x∈S,where S=R/Z=[0,1)is the unit circle, and aim to leverage ideas from our previous work to further … WebModulation of Camassa--Holm equation and reciprocal transformations Abenda, Simonetta ; Grava, Tamara We derive the modulation equations or Whitham equations for the Camassa--Holm (CH) equation. We show that the modulation equations are hyperbolic and admit bi-Hamiltonian structure.
On whitham equations for camassa-holm
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Web1 de set. de 2009 · In this paper we take up the question of a small dispersion limit for the Camassa-Holm equation. The particular limit we study involves a modification of the Camassa-Holm equation, seen in the recent theoretical … WebWell-posedness of higher dimensional Camassa-Holm equations on manifolds with boundary Fran¸cois Gay-Balmaz1 AMS Classification: 37K65, 35Q35, 35Q53, 58D05, …
Web14 de mar. de 2005 · The Camassa–Holm and most members of Whitham's equation family were derived as one-space-dimensional approximations to the irrotational surface water waves in various parameter regimes (perhaps with additional complications such as Coriolis forces included), so one would expect very similar behavior, even though … Web5 de set. de 2009 · Numerical Solution of the Small Dispersion Limit of the Camassa-Holm and Whitham Equations and Multiscale Expansions S. Abenda, T. Grava, C. Klein The small dispersion limit of solutions to the Camassa-Holm (CH) equation is characterized by the appearance of a zone of rapid modulated oscillations.
Web16 de mai. de 2008 · We study the Whitham equations for the Camassa-Holm equation. The equations are neither strictly hyperbolic nor genuinely nonlinear. We are interested … Web15 de nov. de 2006 · We present a Riemann–Hilbert problem formalism for the initial value problem for the Camassa–Holm equation u t − u t x x + 2 ω u x + 3 u u x = 2 u x u x x + …
Web12 de fev. de 2007 · detailed analysis of the situation and compare the Korteweg-de Vries solution quantitatively with asymptotic solutions obtained via the solution of the Hopf and the Whitham equations. We give a qualitative analysis for the Camassa-Holm equation Submission history From: Christian Klein [view email]
WebIn mathematical physics, the Whitham equation is a non-local model for non-linear dispersive waves . The equation is notated as follows : This integro-differential equation … smallwood academy nlWebWe apply the method of nonlinear steepest descent to compute the long-time asymptotics of the Camassa–Holm equation for decaying initial data, completing previous results by … hilde baeyens facebookWeb28 de fev. de 2024 · We determine the stability and instability of a sufficiently small and periodic traveling wave to long wavelength perturbations, for a nonlinear dispersive equation which extends a Camassa-Holm equation to include all the dispersion of water waves and the Whitham equation to include nonlinearities of medium amplitude waves. … smallwood \\u0026 schooler 2006Web5 de out. de 2024 · It is interesting that the FW equation does not only allow traveling wave solutions like the KdV equation, but also possess peakon solutions [11] as some Camassa–Holm type equations. However, the FW equation is not integrable [20] and there is no useful conservation laws which would be used to make estimates of solutions, … hilde baele lochristiWebtopWe derive the modulation equations (Whitham equations) for the Camassa-Holm (CH) equation. We show that the modulation equations are hyperbolic and admit a bi-Hamiltonian structure. Furthermore they are connected by a reciprocal transformation to the hilde bossuytWeb1 de jan. de 2009 · The Camassa–Holm equation u t + ( 3 u + 2 ν) u x − ϵ 2 ( u x x t + 2 u x u x x + u u x x x) = 0, u ( x, 0; ϵ) = u 0 ( x) describes waves in shallow water when … smallwood \u0026 associatesWebThe Camassa–Holm equation has a number of constants of motion arising as eigenvalues of an associated spectral problem. We give a description of the spectral … hilde beast twitch