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# Documents  35C08 | enregistrements trouvés : 4

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## Unresolved problems in the theory of integrable systems Zakharov, Vladimir | CIRM H

Post-edited

Research talks;Partial Differential Equations;Mathematical Physics

In spite of enormous success of the theory of integrable systems, at least three important problems are not resolved yet or are resolved only partly. They are the following:
1. The IST in the case of arbitrary bounded initial data.
2. The statistical description of the systems integrable by the IST. Albeit, the development of the theory of integrable turbulence.
3. Integrability of the deep water equations.
These three problems will be discussed in the talk.
In spite of enormous success of the theory of integrable systems, at least three important problems are not resolved yet or are resolved only partly. They are the following:
1. The IST in the case of arbitrary bounded initial data.
2. The statistical description of the systems integrable by the IST. Albeit, the development of the theory of integrable turbulence.
3. Integrability of the deep water equations.
These three problems will be discussed ...

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## Interactions of solitary waves for the nonlinear Schrödinger equations Martel, Yvan | CIRM H

Multi angle

Research talks;Partial Differential Equations

I will present two cases of strong interactions between solitary waves for the nonlinear Schrödinger equations (NLS). In the mass sub- and super-critical cases, a work by Tien Vinh Nguyen proves the existence of multi-solitary waves with logarithmic distance in time, extending a classical result of the integrable case (1D cubic NLS equation). In the mass-critical case, a work by Yvan Martel and Pierre Raphaël gives a new class of blow up multi-solitary waves blowing up in infinite time with logarithmic rate.
These special behaviours are due to strong interactions between the waves, in contrast with most previous works on multi-solitary waves of (NLS) where interactions do not affect the general behaviour of each solitary wave.
I will present two cases of strong interactions between solitary waves for the nonlinear Schrödinger equations (NLS). In the mass sub- and super-critical cases, a work by Tien Vinh Nguyen proves the existence of multi-solitary waves with logarithmic distance in time, extending a classical result of the integrable case (1D cubic NLS equation). In the mass-critical case, a work by Yvan Martel and Pierre Raphaël gives a new class of blow up ...

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## Skyrme fields, multi-instantons and the $SU(\infty )$-Toda equation Plansangkate, Prim | CIRM H

Multi angle

Research talks;Mathematical Physics

We construct Skyrme fields from holonomy of the spin connection of multi-Taub-NUT instantons with the centres positioned along a line in R3. The domain of our Skyrme fields is the space of orbits of the axial symmetry of the multi-Taub-NUT instantons. We obtain an expression for the induced Einstein-Weyl metric on the space and its associated solution to the $SU(\infty )$-Toda equation.

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## Solitons in two-dimensional shallow water Kodama, Yuji | Society For Industrial And Applied Mathematics 2018

Ouvrage

- xiii; 252 p.
ISBN 978-1-61197-551-2

CBMS-NSF regional conference series in applied mathematics , 0092

Localisation : Collection 1er étage

soliton # vague # dispersion # vague non linéaire dispersive # équation de type Boussinesq # équation de Kadomtsev-Petviashvili (KP) # soliton KP # équation de Burgers # soliton KdV

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