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Modified scattering for the Gross-Pitaevskii equation

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consider that that's an initial conditions is a question and you do corresponding solution then he behaves like the kind of free will rule should apply to of piety Ellen where J. satisfies these equations which actually is simpler than this is a modified scattering results so if you if you will if this that they would not depend on times a year just was a constant demands that we would have a scattering result but here it is his duty to modification and later on we will see you where it appears there is also out of danger the Congress resort which can be seen some of the popular dynamics of the answering a question and this visit stated that if you consider any solution In the solution of this equation then there exists you which satisfies the known nationally accretion such that the source forceful and Bennigan's construct to connivance and support of the precise so if you consider gene which is in its press and smaller and managing the dissolution of the recent and then there exists 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summer supported norms or it's also in lots of with no longer than it's remains a small fall 4 times which are at the are indeed putting new maritime units in so this is occurring in the spirit of the rule of difficult moment home another type of resorts are came reserves so EDS earned and Cooksey enough proved that there exists a came real solutions to secretion so again using the because centuries the therefore that they exist the designated solutions so those remaining more for all times but now only heroes some derided DVDs concerns all its it's more initial conditions and came reserves concerned some of the console but all types of assault this is because it failed solution but the case of the cost was 0 is so this is a picture in to the context of very ridiculous valuables but now if you consider the on the other hand the equation on on the venue expects to scattering results of with me just give you will and this victory this series who considered the question on Monday was the Austrian In the new executives concluding the users and the such results go back to work to need below and into and that he had the idea to consider our product many followers used to tools use situations in between and the study has been initiated by youths with government-issued for foreigners always in the case so the the ideas of following in 1 of the you have the reduces the suspension is to make it so that in the infinity norm in X is less than 1 over to to acquiring follow 1 one-half this is the disposition its unity should believe it will To provide that you will do stated in your solution and then if you consider the nonunion terms like like a potential terror then the staff should behave like the 1 over the Titans you and so I did do they mentioned in these higher Alderman ladies has a larger pool of then this becomes integral but and you can prove scattering reasons and here you are exactly into India limits case and actually do looked around which isn't In these results comes from more than 1 of you which appears here so it's nonsense to consider the issue of a stronger poet this becomes integral and that he had this listened to entreaty appears later constant and here you will see the discounting appeal but here you are just 2 fingers in the case so now and we try to give you an idea so-called weekend makeshift residency reasons appeared slim particles that affected underneath so we consider the profile of fuel so you you conjugate resident your operator then the function as some of the and the questioned whether the new about this being canceled so it looks like this so I don't know if this Jerry depends on dynamite until the season ends and and another to study its you can do work for you to position so boasts in the next by about 19 why you valuable sold to very very for years from X to society of the known this can be written as the researchers and then the weakened so the full year the project to fully of the product is a convolution so you have such talent appearing the commission so this is the sort you here you have the terms of this is the for the Topeka for Yukon call conditions of the moment the moment to here those are the Eigen venues of the senior operator and here is the convolution which appears scenes of the product and honored to be here to give you an idea of the long-time behavior of such terms so he would you can
prove is that using integration by parts so Uganda divided by this fact also integration in time and the actually the is these factories lodged in the day we have a smaller contributions and in any case I can control them using 2 residents assumption by so this is really need immediate loss of their relatives but that more is so the 1st time assumption is that you can 2 of terms in which our key and huge congress must send a signal to the world and this implies that has the same length as queue up to presentations to see what I have read in the privacy of key and can lead us and maybe it's just 2 them we tend to to see it so here I had the control I said that I have to go to evade assert largest and favored here on the UC when you want to study months union towns uh you you you are not allowed to work to heat so do many of the frequencies you we won't so if you want to study say you're a term which means they could enjoy your from using the devil you know when you want to make summer and estimate of heat so as to whether to estimated read by duality if you have full terms so a you V and Avenue and you want to make a good decision made so you do with regularity so that you can do it you you're not allowed to hit ready when the 1st time because it's it's 1 of the Serbian it's at this function church so do the 1st 2 largest is not enough again and the 2nd largest so please is not that loans also because if you you want to do the same the same estimated that consumer richest norms then you would like to heat on you on the do you determine which hazardous instruments so the 2nd is also not an old but then Uganda heats here and here you you may lose to the derivative I you have the denoted by John and this shows that then you up people into work to obtain a good solutions .period argument in some gunmen this is a roughly speaking to the thing and didn't the his teammates is served largess was crucial and previously used by you walks in and by you can bet on collaborators so this was a restriction to the reasoning terms and the 2nd to restriction come summer phase of formula we especially face from solar here you you were trying to arrest the test in the face to the phases find isn't it to cap on and on so this faces questions tension on the eve of counterparties 0 and then so no no nearer it looks like a brother to restore the England died in the large enough so you have this factor P 1 nobody comes from the fastest in the phrase from Lyon deep so would do to mentioned here are often in the cap attack and then you still have to do contribution reserve a typist was 0 so it's a F Q but with side and flew off part of CSI and if this parts and and here we have the think of the reason systems so we see how well we comes from and the view of the value over to you can cancel out by a change of idea violence here you despite you have some questions it is single 5 remaining minutes and really just the government on some other mothers Yukon study research ideas so such arguments also walk on the moon for that money faults I cross tools so you take that their stand on his feet so this has been the mentioning of people and he couldn't answer confrontation here so this has been done for the Mexicans because you have to wave of character so the why you absolute value and it has been done by your height and should and in this context the reason and so the question which is associated is disfiguring Christians and saddled her to construct a growing old
you can also study system so it is soul the couple and their Tennessee commissions and other diseases under investigation by you and the dog and the lesser of 2 and the reserves I honey and the gentleman we we have obtained results for the for the Gorski today equations which which is there and there is a question that freezer confining potential source you can refer to the retreat to to their so you have a potential which is as quick and is a question is that is studied in the context of globalization strangling the sites where wherever we wish to use to the Europe received cigar-shaped condensates and in this context we can prove also that you have a modify scattering results and under underlying reason to question is also well-known known he's related to the West Longo questions the lowest level in normally questions and this notice to construct some practical solutions to produce a question I think you he said he knew what was going on and on and on and on the parameters for the same Pereira explained that in the last line work at the meeting so you're equation for G previous 0 an increase for all involve 1 parameter yes yes I did he said the value of it's just the cost of this convolution of 3 functions to parameters Cienega of the but the stationary phase ideas CDC's worried about needed what students interest so that I have a question about the Our equation which is not 1 equation is in fact a continuum family relations each 1 needs a solution the Red Sea is a proud yes and for Oxy the solution yes the renewed resonance conditions which resists the French no I gave you and you walk on the question resolved the and then I can from too a candidate what sentiments studied the question with the parliament I I I do not have to compete description Eichinger practical solution on the question which does not depend on the perimeter and Nikon added to the point so I can do 1 parameter 160 years several C is not always for all to see yeah sentiments he claimed that the bureaucrats at the Ministry of discussion at the venue on also questioned even work on the questions of pop OK well so long as you hear in his 1st day in the future and my
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Formale Metadaten

Titel Modified scattering for the Gross-Pitaevskii equation
Serientitel Trimestre Ondes Non Linéaires - May conference
Teil 04
Anzahl der Teile 21
Autor Thomann, Laurent
Lizenz CC-Namensnennung 3.0 Unported:
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DOI 10.5446/20766
Herausgeber Institut des Hautes Études Scientifiques (IHÉS)
Erscheinungsjahr 2016
Sprache Englisch

Inhaltliche Metadaten

Fachgebiet Mathematik
Abstract We consider the cubic nonlinear Schrödinger equation with harmonic trapping. In the case when all but one directions are trapped, we prove modified scattering and construct modified wave operators for small initial and final data respectively. Actually, we prove that the asymptotic behavior of the solutions is given by a simpler equation, depending on the resonances of the GP equation, and we exhibit some particular solutions of it.

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