305 research outputs found
Traveling waves for nonlinear Schr\"odinger equations with nonzero conditions at infinity, II
We prove the existence of nontrivial finite energy traveling waves for a
large class of nonlinear Schr\"odinger equations with nonzero conditions at
infinity (includindg the Gross-Pitaevskii and the so-called "cubic-quintic"
equations) in space dimension . We show that minimization of the
energy at fixed momentum can be used whenever the associated nonlinear
potential is nonnegative and it gives a set of orbitally stable traveling
waves, while minimization of the action at constant kinetic energy can be used
in all cases. We also explore the relationship between the families of
traveling waves obtained by different methods and we prove a sharp nonexistence
result for traveling waves with small energy.Comment: Final version, accepted for publication in the {\it Archive for
Rational Mechanics and Analysis.} The final publication is available at
Springer via http://dx.doi.org/10.1007/s00205-017-1131-
Travelling waves for the Gross-Pitaevskii equation II
The purpose of this paper is to provide a rigorous mathematical proof of the
existence of travelling wave solutions to the Gross-Pitaevskii equation in
dimensions two and three. Our arguments, based on minimization under
constraints, yield a full branch of solutions, and extend earlier results,
where only a part of the branch was built. In dimension three, we also show
that there are no travelling wave solutions of small energy.Comment: Final version accepted for publication in Communications in
Mathematical Physics with a few minor corrections and added remark
Global well-posedness of the KP-I initial-value problem in the energy space
We prove that the KP-I initial value problem is globally well-posed in the
natural energy space of the equation
Numerical study of oscillatory regimes in the Kadomtsev-Petviashvili equation
The aim of this paper is the accurate numerical study of the KP equation. In
particular we are concerned with the small dispersion limit of this model,
where no comprehensive analytical description exists so far. To this end we
first study a similar highly oscillatory regime for asymptotically small
solutions, which can be described via the Davey-Stewartson system. In a second
step we investigate numerically the small dispersion limit of the KP model in
the case of large amplitudes. Similarities and differences to the much better
studied Korteweg-de Vries situation are discussed as well as the dependence of
the limit on the additional transverse coordinate.Comment: 39 pages, 36 figures (high resolution figures at
http://www.mis.mpg.de/preprints/index.html
The phase shift of line solitons for the KP-II equation
The KP-II equation was derived by [B. B. Kadomtsev and V. I.
Petviashvili,Sov. Phys. Dokl. vol.15 (1970), 539-541] to explain stability of
line solitary waves of shallow water. Stability of line solitons has been
proved by [T. Mizumachi, Mem. of vol. 238 (2015), no.1125] and [T. Mizumachi,
Proc. Roy. Soc. Edinburgh Sect. A. vol.148 (2018), 149--198]. It turns out the
local phase shift of modulating line solitons are not uniform in the transverse
direction. In this paper, we obtain the -bound for the local phase
shift of modulating line solitons for polynomially localized perturbations
Representation formula for stochastic Schrödinger evolution equations and applications
Important marine areas for the conservation of northern rockhopper penguins within the Tristan da Cunha Exclusive Economic Zone
The designation of Marine Protected Areas has become an important approach to conserving marine ecosystems that relies on robust information on the spatial distribution of biodiversity. We used GPS tracking data to identify marine Important Bird and Biodiversity Areas (IBAs) for the endangered northern rockhopper penguin Eudyptes moseleyi within the Exclusive Economic Zone (EEZ) of Tristan da Cunha in the South Atlantic. Penguins were tracked throughout their breeding season from 3 of the 4 main islands in the Tristan da Cunha group. Foraging trips remained largely within the EEZ, with the exception of those from Gough Island during the incubation stage. We found substantial variability in trip duration and foraging range among breeding stages and islands, consistent use of areas among years and spatial segregation of the areas used by neighbouring islands. For colonies with no or insufficient tracking data, we defined marine IBAs based on the mean maximum foraging range and merged the areas identified to propose IBAs around the Tristan da Cunha archipelago and Gough Island. The 2 proposed marine IBAs encompass 2% of Tristan da Cunhaâs EEZ, and are used by all northern rockhopper penguins breeding in the Tristan da Cunha group, representing ~90% of the global population. Currently, the main threat to northern rockhopper penguins within the Tristan da Cunha EEZ is marine pollution from shipping, and the risk of this would be reduced by declaring waters within 50 nautical miles of the coast as âAreas To Be Avoided
Geometric numerical schemes for the KdV equation
Geometric discretizations that preserve certain Hamiltonian structures at the
discrete level has been proven to enhance the accuracy of numerical schemes. In
particular, numerous symplectic and multi-symplectic schemes have been proposed
to solve numerically the celebrated Korteweg-de Vries (KdV) equation. In this
work, we show that geometrical schemes are as much robust and accurate as
Fourier-type pseudo-spectral methods for computing the long-time KdV dynamics,
and thus more suitable to model complex nonlinear wave phenomena.Comment: 22 pages, 14 figures, 74 references. Other author's papers can be
downloaded at http://www.lama.univ-savoie.fr/~dutykh
«La relation de limitation et dâexception dans le français dâaujourdâhui : exceptĂ©, sauf et hormis comme pivots dâune relation algĂ©brique »
Lâanalyse des emplois prĂ©positionnels et des emplois conjonctifs dâ âexceptĂ©â, de âsaufâ et dâ âhormisâ permet dâenvisager les trois prĂ©positions/conjonctions comme le pivot dâun binĂŽme, comme la plaque tournante dâune structure bipolaire. PlacĂ©es au milieu du binĂŽme, ces prĂ©positions sont forcĂ©es par leur sĂ©mantisme originaire dĂ»ment mĂ©taphorisĂ© de jouer le rĂŽle de marqueurs dâinconsĂ©quence systĂ©matique entre lâĂ©lĂ©ment se trouvant Ă leur gauche et celui qui se trouve Ă leur droite. Lâopposition qui surgit entre les deux Ă©lĂ©ments nâest donc pas une incompatibilitĂ© naturelle, intrinsĂšque, mais extrinsĂšque, induite. Dans la plupart des cas (emplois limitatifs), cette opposition prend la forme dâun rapport entre une « classe » et le « membre (soustrait) de la classe », ou bien entre un « tout » et une « partie » ; dans dâautres (emplois exceptifs), cette opposition se manifeste au contraire comme une attaque de front portĂ©e par un « tout » Ă un autre « tout ». De plus, lâinconsĂ©quence induite mise en place par la prĂ©position/conjonction paraĂźt, en principe, tout Ă fait insurmontable. Dans lâassertion « les Ă©cureuils vivent partout, sauf en Australie » (que lâon peut expliciter par « Les Ă©cureuils vivent partout, sauf [quâils ne vivent pas] en Australie »), la prĂ©position semble en effet capable dâimpliquer le prĂ©dicat principal avec signe inverti, et de bĂątir sur une telle implication une sorte de sous Ă©noncĂ© qui, Ă la rigueur, est totalement inconsĂ©quent avec celui qui le prĂ©cĂšde (si « les Ă©cureuils ne vivent pas en Australie », le fait quâils « vivent partout » est faux). NĂ©anmoins, lâanalyse montre quâalors que certaines de ces oppositions peuvent enfin ĂȘtre dĂ©passĂ©es, dâautres ne le peuvent pas. Câest, respectivement, le cas des relations limitatives et des relations exceptives. La relation limitative, impliquant le rapport « tout » - « partie », permet de rĂ©soudre le conflit dans les termes dâune somme algĂ©brique entre deux sous Ă©noncĂ©s pourvus de diffĂ©rent poids informatif et de signe contraire. Les valeurs numĂ©riques des termes de la somme Ă©tant dĂ©sĂ©quilibrĂ©es, le rĂ©sultat est toujours autre que zĂ©ro. La relation exceptive, au contraire, qui nâimplique pas le rapport « tout » - « partie », nâest pas capable de rĂ©soudre le conflit entre deux sous Ă©noncĂ©s pourvus du mĂȘme poids informatif et en mĂȘme temps de signe contraire : les valeurs numĂ©riques des termes de la somme Ă©tant symĂ©triques et Ă©gales, le rĂ©sultat sera toujours Ă©quivalent Ă zĂ©ro
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