{"paper":{"title":"On the classification of conditionally integrable evolution systems in (1+1) dimensions","license":"","headline":"","cross_cats":["hep-th","math-ph","math.MP"],"primary_cat":"nlin.SI","authors_text":"A. Sergyeyev","submitted_at":"2004-10-18T22:03:02Z","abstract_excerpt":"We generalize earlier results of Fokas and Liu and find all locally analytic (1+1)-dimensional evolution equations of order $n$ that admit an $N$-shock type solution with $N\\leq n+1$.\n  To this end we develop a refinement of the technique from our earlier work (A. Sergyeyev, J. Phys. A: Math. Gen, 35 (2002), 7653--7660), where we completely characterized all (1+1)-dimensional evolution systems $\\bi{u}_t=\\bi{F}(x,t,\\bi{u},\\p\\bi{u}/\\p x,...,\\p^n\\bi{u}/\\p x^n)$ that are conditionally invariant under a given generalized (Lie--B\\\"acklund) vector field $\\bi{Q}(x,t,\\bi{u},\\p\\bi{u}/\\p x,...,\\p^k\\bi{u}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"nlin/0410029","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"}