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BLOWDISOL

Financiado

Cerrado

BLOW UP DISPERSION AND SOLITONS

"Many physical models involve nonlinear dispersive problems, like wave or laser propagation, plasmas, ferromagnetism, etc. So far, the mathematical under- standing of these equations is rather poor. In particular, we know little a... ver más

31/03/2017

UCP

2M€

Presupuesto del proyecto: 2M€

Líder del proyecto

UNIVERSITE DE CERGYPONTOISE No se ha especificado una descripción o un objeto social para esta compañía.

TRL 4-5

Fecha límite participación Sin fecha límite de participación.

Financiación concedida El organismo FP7 notifico la concesión del proyecto el día 2017-03-31 No tenemos la información de la convocatoria

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1 Participantes

UCP

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Líder del proyecto

UNIVERSITE DE CERGYPONTOISE No se ha especificado una descripción o un objeto social para esta compañía.

TRL 4-5

Presupuesto del proyecto 2M€

Fecha límite de participación Sin fecha límite de participación.

Descripción del proyecto "Many physical models involve nonlinear dispersive problems, like wave or laser propagation, plasmas, ferromagnetism, etc. So far, the mathematical under- standing of these equations is rather poor. In particular, we know little about the detailed qualitative behavior of their solutions. Our point is that an apparent com- plexity hides universal properties of these models; investigating and uncovering such properties has started only recently. More than the equations themselves, these univer- sal properties are essential for physical modelisation. By considering several standard models such as the nonlinear Schrodinger, nonlinear wave, generalized KdV equations and related geometric problems, the goal of this pro- posal is to describe the generic global behavior of the solutions and the proﬁles which emerge either for large time or by concentration due to strong nonlinear eﬀects, if pos- sible through a few relevant solutions (sometimes explicit solutions, like solitons). In order to do this, we have to elaborate diﬀerent mathematical tools depending on the context and the speciﬁcity of the problems. Particular emphasis will be placed on - large time asymptotics for global solutions, decomposition of generic solutions into sums of decoupled solitons in non integrable situations, - description of critical phenomenon for blow up in the Hamiltonian situation, stable or generic behavior for blow up on critical dynamics, various relevant regularisations of the problem, - global existence for defocusing supercritical problems and blow up dynamics in the focusing cases. We believe that the PI and his team have the ability to tackle these problems at present. The proposal will open whole ﬁelds of investigation in Partial Diﬀerential Equations in the future, clarify and simplify our knowledge on the dynamical behavior of solutions of these problems and provide Physicists some new insight on these models."

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