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arXiv:2005.01022v1 [math.AP] 3 May 2020

arXiv:2005.01022v1 [math.AP] 3 May 2020

introduced in Ratliff [30,28]. However, multiphase Whitham modulation theory has a rich history. Multiphase WMEs were rst introduced and studied by Ablowitz & Benney [1], in the context of scalar nonlinear wave equations, where the appearance of small divisors was noted. For integrable systems small divisors disappear: multiphase averaging and the

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Whitham's modulation equations and stability of periodic ...

Whitham

0) and the first-order Whitham’s modulation system: the hyper-bolicity of such a system provides a necessary condition of spectral stability. Under a condition of strict hyperbolicity, we show that eigenvalues are indeed analytic in the neighborhood of the origin and that their expansion up to second order is connected to a vis-

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Whitham’s Modulation Equations and Stability of Periodic ...

Whitham’s Modulation Equations and Stability of Periodic ...

Whitham’s Modulation Equations and Stability of Periodic Wave Solutions of the Korteweg-de Vries-Kuramoto-Sivashinsky Equation Pascal Noble L.Miguel Rodriguesy Keywords: modulation; periodic traveling waves; Kuramoto-Sivashinsky equations, Korteweg-de Vries equations; Bloch decomposition. 2000 MR Subject Classi cation: 35Q53, 35B10, 35B35, 35P10. Abstract We study the spectral stability of ...

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Whitham’s Modulation Equations and Stability of Periodic ...

Whitham’s Modulation Equations and Stability of Periodic ...

0 and Floquet parameter 0) and the first order Whitham’s modulation system: the hy-perbolicity of such a system provides a necessary condition of spectral stability. Under a condition of strict hyperbolicity, we show that eigenvalues are indeed analytic in the neighborhood of the origin and that their expansion up to second order is connected to a viscous correction of the Whitham’s ...

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Whitham’s equations for modulated roll-waves in shallow ows

Whitham’s equations for modulated roll-waves in shallow ows

We first derive the so-called Whitham’s averaged modulation equations and relate the well-posedness of this set of equations to the spectral stability problem in the small Floquet-number limit. We then fully validate such a system and in particular, we are able to construct solutions to the shallow water equations in the neighbourhood of modulated roll-waves profiles that exist for ...

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Whitham modulation equations and application

Whitham modulation equations and application

Whitham modulation equations and application to small dispersion asymptotics and long time asymptotics of nonlinear dispersive equations Tamara Grava1,2 1SISSA, Via Bonomea 265, 34136 Trieste, Italy, [email protected] 2School of Mathematics, University of Bristol, Bristol BS8 1TW, UK January 3, 2017 Abstract In this chapter we review the theory of modulation equations or Whitham equa-tions for ...

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Lecture 10: Whitham Modulation Theory

Lecture 10: Whitham Modulation Theory

The Whitham modulation theory provides an asymptotic method for studying slowly varying periodic waves, and is essentially a nonlinear WKB theory. Equations are derived which describe the slow evolution of the governing parameters for these nonlinear periodic waves (such as the amplitude, wavelength, frequency, etc.), and are called the modulation (or Whitham) equations. The Whitham equations ...

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Nonlocalized modulation of periodic reaction di usion ...

Nonlocalized modulation of periodic reaction di usion ...

Whitham modulation equation of a type derived formally in, e.g., [S1,DSSS, W]. This not only gives rigorous validation of the formal Whitham approx-imation in the strong sense of showing that it describes time-asymptotic behavior, but, through the explicit prescription of initial data coming from our analysis, also gives new information of predictive value not available from the formal ...

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DOSSIER DR2 CNRS Pascal NOBLE - math.univ-lyon1.fr

DOSSIER DR2 CNRS Pascal NOBLE - math.univ-lyon1.fr

[S1] P. Noble, L.M. Rodrigues: Whitham's modulation equations and Stability of Periodic Wave Solutions of the Generalized Kuramoto-Sivashinsky equations (2011) submitted. [S2] P. Noble, L.M. Rodrigues: Whitham's equations for modulated roll-waves in shallow flows, en collaboration avec L.-M. Rodrigues (ICJ Lyon), (2010) submitted, arXiv:1011.2296.

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Sujet de thèse: Stabilitédesrouleauxdanslesfilmsminces

Sujet de thèse: Stabilitédesrouleauxdanslesfilmsminces

cesdernièresfournissantuneapproximationpourd’écrireladynamiquedesfilmsmincesdes équations,pluscomplètesmaistropcomplexes,d’Euleràsurfacelibre ...

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Etude de l’interaction ondes de gravité - courants ...

Etude de l’interaction ondes de gravité - courants ...

• les études de la modulation d’ondes dans un fluide de profondeur infinie. 2 Interaction houle/courant dans les zones côtières . Dans le cadre de l’approximation de grandes longueurs d’onde en fluides peu profonds les équations de Boussinesq (Whitham, 1974) et de GreenNaghdi (Green- -Naghdi, 1976), aussi appelées équations de Serre ou de SuGardner ont été largement étudiées ...

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