On whitham equations for camassa-holm
WebWe study the generalized Camassa-Holm equation which contains the Camassa-Holm (CH) equation and Novikov equation as special cases with the periodic boundary condition. We get a blow-up scenario and obtain the global existence of strong and weak solutions under suitable assumptions, respectively. Then, we construct the periodic peaked … WebtopWe 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
On whitham equations for camassa-holm
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WebThe Whitham equations are a system of hydrodynamic type equations [12] and in the Riemann invariant coordinates take the form ui t= v i(u)ui x , i= 1,...,N, u = (u 1,...,u N). The original evolution system is usually Lagrangian or Hamiltonian and this prop- erty is usually inherited by the equations of slow modulations. Web1 de mar. de 2006 · On Whitham Equations for Camassa-Holm Abenda, S. Grava, T. Klein, C. Abstract The solution of the Cauchy problem for the Camassa-Holm equation …
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. Web13 de fev. de 2024 · The aim of this paper is to analyze the water waves problem for uneven bottom under the influence of surface tension. For that, we consider an asymptotic model of the 1D Green-Naghdi equations in Camassa-Holm scale and derive in a formal way by using the Whitham technique the Camassa-Holm equation under the influence of …
WebWe 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 Boutet de Monvel and Shepelsky. WebIn this paper, we present some preliminary work in the direction of numerically compare the solution to the Cauchy problem of the Camassa–Holm equation in the limit ε → 0 and the approximate solution which should be described by the corresponding Whitham equations.
WebWell-posedness of higher dimensional Camassa-Holm equations on manifolds with boundary Fran¸cois Gay-Balmaz1 AMS Classification: 37K65, 35Q35, 35Q53, 58D05, 58B20, 53D25. Keywords: Camassa-Holm equations, well-posedness, Sobolev diffeomorphism group, weak Riemannian metrics, geodesic spray, Euler-Poincar´e …
Web5 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, … how many christmas trees are soldWeb2 de mai. de 2007 · We survey some topics involving the Whitham equations, concentrating on the role of ψψ ∗ (or square eigenfunctions) in averaging, where ψ is the … how many christmas trees are sold yearlyWeb1 de jan. de 2009 · We study the Whitham equations for the Camassa–Holm equation. The equations are neither strictly hyperbolic nor genuinely nonlinear. We are interested … high school menlo parkWeb21 de mai. de 2024 · We analyze stability of conservative solutions of the Cauchy problem on the line for the Camassa–Holm (CH) equation. Generically, the solutions of the CH equation develop singularities with steep gradients while preserving continuity of … high school men outfitsWeb1 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 … high school memory booksWeb15 de nov. de 2007 · These Whitham equations are quasilinear hyperbolic equations and they describe the averaged dynamics of the rapid oscillations which appear in the … high school men\u0027s volleyball rankings 2018WebWell-posedness of higher dimensional Camassa-Holm equations on manifolds with boundary Fran¸cois Gay-Balmaz1 AMS Classification: 37K65, 35Q35, 35Q53, 58D05, … how many christmas trees sold in uk