On whitham equations for camassa-holm
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 WebA numerical study of this limit for smooth hump-like initial data provides strong evidence for the validity of the conjecture that the phase of the asymptotic solution of the Camassa–Holm equation depends on the physical coordinates via the Whitham equations. Expand 3 PDF Save Alert
On whitham equations for camassa-holm
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Web15 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 … 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 in the initial value problem of the Whitham equations. When the initial values are given by a step function, the Whitham solution is self-similar. When the initial values are given by a …
Web21 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 … 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.
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. 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.
WebThe Camassa-Holm equation has a number of constants of motion arising as eigen-values of an associated spectral problem. We give a description of the spectral picture and …
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. crypto textbookWeb25 de nov. de 2024 · The nonlinear Schrödinger (NLS) equation and the Whitham modulation equations both describe slowly varying, locally periodic nonlinear wavetrains, albeit in differing amplitude‐frequency domains. In… 13 PDF View 2 excerpts, references methods Multiphase averaging and the inverse spectral solution of the Korteweg—de … crystal apple award winnersWebModulation 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. crypto text scamWeb28 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. … crystal application toolWeb10 de dez. de 1997 · Some tricks from the symmetry-toolbox for nonlinear equations: generalizations of the Camassa–Holm equation Phys. D , 95 ( 1996 ) , pp. 243 - 296 … crypto textureWebWell-posedness of higher dimensional Camassa-Holm equations on manifolds with boundary Fran¸cois Gay-Balmaz1 AMS Classification: 37K65, 35Q35, 35Q53, 58D05, … crystal apple cucumbers in australiaWeb关于带有弱耗散项的camassa-holm方程解的性质,一元二次方程性质,方程的性质,一元二次方程的性质,vaxholm,ian holm,stockholm,henrietta holm,drottningholm,holly holm,chisholm crystal apple cucumber plants