{"paper":{"title":"Existence and multiplicity of normalized solutions for the generalized Kadomtsev-Petviashvili equation in $\\mathbb{R}^2$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Chao Ji, Claudianor O. Alves, Rui Ding","submitted_at":"2025-06-05T12:42:44Z","abstract_excerpt":"In this paper, we study the existence and {multiplicity} of nontrivial solitary waves for the generalized Kadomtsev-Petviashvili equation with prescribed {$L^2$-norm} \\begin{equation*}\\label{Equation1}\n  \\left\\{\\begin{array}{l}\n  \\left(-u_{x x}+D_x^{-2} u_{y y}+\\lambda u-f(u)\\right)_x=0,{\\quad x \\in \\mathbb{R}^2, } \\\\[10pt]\n  \\displaystyle \\int_{\\mathbb{R}^2}u^2 d x=a^2,\n  \\end{array}\\right.%\\tag{$\\mathscr E_\\lambda$} \\end{equation*} where $a>0$ and $\\lambda \\in \\mathbb{R}$ is an unknown parameter that appears as a Lagrange multiplier. For the case $f(t)=|t|^{q-2}t$, with $2<q<\\frac{10}{3}$ ($"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.04967","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.04967/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}