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arXiv · 1705.05964

Regularizing nonlinear Schroedinger equations through partial off-axis variations

Paolo Antonelli·Jack Arbunich·Christof Sparber
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Abstract

We study a class of focusing nonlinear Schroedinger-type equations derived recently by Dumas, Lannes and Szeftel within the mathematical description 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 study the well-posedness theory for such models and obtain a regularizing effect, 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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Paolo Antonelli, Jack Arbunich, Christof Sparber. 2019-01-18. Regularizing nonlinear Schroedinger equations through partial off-axis variations. https://arxiv.org/abs/1705.05964

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