{"paper":{"title":"On a class of derivative Nonlinear Schr\\\"odinger-type equations in two spatial dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"C. Klein, C. Sparber, J. Arbunich","submitted_at":"2018-05-31T07:18:52Z","abstract_excerpt":"We present analytical results and numerical simulations for a class of nonlinear dispersive equations in two spatial dimensions. These equations are of (derivative) nonlinear Schr\\\"odinger type and have recently been obtained in \\cite{DLS} in the context of nonlinear optics. In contrast to the usual nonlinear Schr\\\"odinger equation, this new model incorporates the additional effects of self-steepening and partial off-axis variations of the group velocity of the laser pulse. We prove global-in-time existence of the corresponding solution for various choices of parameters, extending earlier resu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.12351","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}