REGULARIZING NONLINEAR SCHRO ̈DINGER EQUATIONS THROUGH PARTIAL OFF-AXIS VARIATIONS
PublisherSociety for Industrial and Applied Mathematics
MetadataShow full item record
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 . 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 .
CitationAntonelli, 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
Date available in INDIGO2019-06-10T17:58:34Z
The following license files are associated with this item: