Centre de Physique Théorique

Agenda

Mercredi 22 novembre 2017

11h00 – 12h00, Amphi 5 du CPT

Asymptotics in the Problem on the Run-Up of Long Waves on a Shallow Beach

Vladimir Nazaikinskii (Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences)

Résumé

We discuss near-boundary asymptotics for the solution of the Cauchy
problem for a degenerate wave equation with localized initial data
describing the run-up of long waves (e.g., tsunami waves) on a
shallow beach in the linear approximation. We show that problems of
this type are related to Dirac’s idea, realized by Fock more than
50 years ago, about the quantization of classical canonical
transformations.

The talk is based on joint work with S.Yu. Dobrokhotov and A.A.
Tolchennikov. The research was supported by the Russian Science
Foundation (project 16-11-10282).

14h00 – 15h00, Amphi 5 du CPT

Singular "Punctured" Lagrangian Manifolds and the Asymptotics of Linear Waves near the Leading Edge Front

Serguei Dobrokhotov (Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences)

Résumé

We consider the so-called Cauchy-Poisson problem in a basin with
uneven bottom for the propagation of surface water waves created by
a localized initial perturbation. We show that the asymptotic
solutions of such problems are associated with singular "punctured"
Lagrangian manifolds. The boundary of such a manifold can be viewed
as a new type of caustic (Lagrangian singularity) and determines
the leading front edge. We present efficient formulas for the waves
in a neighborhood of these objects, which permits easily analyzing
the dependence of the wave amplitude on the depth and dispersion.

The talk is based on joint work with V.E.Nazaikinskii,
S.Ya.Sekerzh-Zen’kovich and A.A. Tolchennikov.

Agenda