Masayuki Hayashi (seminarimap.wixsite.com)

--> Titolo: Travelling waves for a nonlinear Schrodinger system with quadratic interaction

--> Abstract: Solitary waves (solitons, standing waves, travelling waves) are known to play a fundamental role in the analysis of nonlinear dispersive equations. First, we briefly explain nonlinear dispersive equations and solitary waves by using the nonlinear Schrodinger equation as an example. Next, as an introduction of recent results obtained by the speaker (jointly with N. Fukaya and T. Inui), we consider travelling waves of a nonlinear Schrodinger system with quadratic interaction. When the mass constants satisfy a certain condition, the system has no specific symmetry such as Galilean or pseudoconformal symmetry, which is of particular interest. We construct travelling wave solutions by variational methods, and also show global existence for oscillating large data as an application. We see that our results essentially come from the lack of Galilean invariance in the system. Finally, I will introduce a few open problems and interesting relevance to other types of nonlinear dispersive equations.

Ricordiamo che questi seminari sono aperti a tuttə: la prima metà del seminario introduce i concetti e gli strumenti necessari per la seconda metà, dedicata agli argomenti di ricerca.

Per altre informazioni, visitate il nostro sito:
https://seminarimap.wixsite.com/seminarimap

A presto,

Gli organizzatori:
Daniele Barbera
Jeremy Mirmina
Mario Rastrelli
Leonardo Roveri
Luciano Sciaraffia

- o - o - o - o - o - o - o - o - o - o - o - o - o - o - o -

>>> English Version <<<

Dear all,

Here the announcement of the next MAP seminar:

--> Speaker:  Masayuki Hayashi

--> Date: Wednesday 02 May, 17:00

--> Where: Aula Seminari, Dipartimento di Matematica (Pisa) and Online on Gmeet:

Masayuki Hayashi (seminarimap.wixsite.com)

--> Title: Travelling waves for a nonlinear Schrodinger system with quadratic interaction

--> Abstract:  Solitary waves (solitons, standing waves, travelling waves) are known to play a fundamental role in the analysis of nonlinear dispersive equations. First, we briefly explain nonlinear dispersive equations and solitary waves by using the nonlinear Schrodinger equation as an example. Next, as an introduction of recent results obtained by the speaker (jointly with N. Fukaya and T. Inui), we consider travelling waves of a nonlinear Schrodinger system with quadratic interaction. When the mass constants satisfy a certain condition, the system has no specific symmetry such as Galilean or pseudoconformal symmetry, which is of particular interest. We construct travelling wave solutions by variational methods, and also show global existence for oscillating large data as an application. We see that our results essentially come from the lack of Galilean invariance in the system. Finally, I will introduce a few open problems and interesting relevance to other types of nonlinear dispersive equations.

We remind that these seminars are addressed to everybody: the first half of the seminar is dedicated to the introduction of notions and tools needed in the second half, which is focused on research topics.

For more information, check our website:

https://seminarimap.wixsite.com/seminarimap

See you soon,

The organizers:
Daniele Barbera
Jeremy Mirmina
Mario Rastrelli
Leonardo Roveri
Luciano Sciaraffia