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REGULARIZING NONLINEAR SCHRO ̈DINGER EQUATIONS THROUGH PARTIAL OFF-AXIS VARIATIONS

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posted on 10.06.2019 by PAOLO ANTONELLI, JACK ARBUNICH, CHRISTOF SPARBER
We study a class of focusing nonlinear Schr ̈odinger-type equations derived recently by Dumas, Lannes and Szeftel within the mathematical de- scription of high intensity laser beams [7]. These equations incorporate the possibility of a (partial) off-axis variation of the group velocity of such laser beams through a second order partial differential operator acting in some, but not necessarily all, spatial directions. We investigate the initial value problem for such models and obtain global well-posedness in L2-supercritical situations, even in the case of only partial off-axis dependence. This provides an answer to an open problem posed in [7].

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Copyright @ Society for Industrial and Applied Mathematics

Citation

Antonelli, P., Arbunich, J., & Sparber, C. (2019). Regularizing nonlinear Schrödinger equations through partial off-axis variations. SIAM Journal on Mathematical Analysis, 51(1), 110-130. doi:10.1137/17M1131313

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Society for Industrial and Applied Mathematics

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en_US

issn

0036-1410

Issue date

29/04/2019

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