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Firstly, we prove that the Cauchy problem for generalized KP-I equation \\begin{eqnarray*}\n  u_{t}+|D_{x}|^{\\alpha}\\partial_{x}u+\\partial_{x}^{-1}\\partial_{y}^{2}u+\\frac{1}{2}\\partial_{x}(u^{2})=0,\\alpha\\geq4\n  \\end{eqnarray*} is locally well-posed in the anisotropic Sobolev spaces$ H^{s_{1},\\>s_{2}}(\\R^{2})$ with $s_{1}>-\\frac{\\alpha-1}{4}$ and $s_{2}\\geq 0$. Secondly, we prove that the problem is globally well-posed in $H^{s_{1},\\>0}(\\R^{2})$ with $s_{1}>-\\frac{(\\alpha-1)(3\\alpha-4)}{4(5\\alpha+3)}$ if $4\\leq \\alpha \\leq5$. Finally, we prove that the probl"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1709.01983","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-06T20:22:26Z","cross_cats_sorted":[],"title_canon_sha256":"e9fece0f2d1b90954c80d0be7355ec5410026f86a06e01c02f14219f8d4ada1b","abstract_canon_sha256":"11ee437c160bf9e0fdc3fe7324455f114c67616f2f7f8a2c3ddeddf5c13d880a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:34:41.244452Z","signature_b64":"jvBvd0AFf1fnxT88KBsTu6f5MCPBiDDx+YK7MABl9HchsjDM1a8YObr8St6vyjlQvV9tJPERAxX6EimkDtIjAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4e39c5aaa0dfc990bc9a6e815120eb965ec3d39d641ee9aba648aab34c948015","last_reissued_at":"2026-05-18T00:34:41.243872Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:34:41.243872Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Cauchy problem for two dimensional generalized Kadomtsev-Petviashvili-I equation in anisotropic Sobolev spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jianhua Huang, Jinqiao Duan, Wei Yan, Yongsheng Li","submitted_at":"2017-09-06T20:22:26Z","abstract_excerpt":"The goal of this paper is three-fold. Firstly, we prove that the Cauchy problem for generalized KP-I equation \\begin{eqnarray*}\n  u_{t}+|D_{x}|^{\\alpha}\\partial_{x}u+\\partial_{x}^{-1}\\partial_{y}^{2}u+\\frac{1}{2}\\partial_{x}(u^{2})=0,\\alpha\\geq4\n  \\end{eqnarray*} is locally well-posed in the anisotropic Sobolev spaces$ H^{s_{1},\\>s_{2}}(\\R^{2})$ with $s_{1}>-\\frac{\\alpha-1}{4}$ and $s_{2}\\geq 0$. Secondly, we prove that the problem is globally well-posed in $H^{s_{1},\\>0}(\\R^{2})$ with $s_{1}>-\\frac{(\\alpha-1)(3\\alpha-4)}{4(5\\alpha+3)}$ if $4\\leq \\alpha \\leq5$. 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