lundi 31 mai  à 16h00 salle B014

Intervenant: D. Shepelsky
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 Institut de Basses Temperatures de Kharkiv, Ukraine

Titre:
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Long-time asymptotics for the Camassa-Holm equation on the line

Resume:
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We will present a detailed long-time asymptotics of solutions
of the Cauchy problem for the Camassa-Holm equation
$u_t-u_{txx}+2\omega u_x+3uu_x=2u_xu_{xx}+uu_{xxx}$,
which is a model equation for shallow water wave propagation.
It turns out that the form of the asymptotics is qualitatively different in 4 different
sectors of the half-plane $-\infty<x<\infty$, $t>0$. Besides, there are
transition regions, where the asymptotics also has specific form.
The method is the adaptation of the inverse scattering transform method
in the form of a Riemann-Hilbert problem.