{"paper":{"title":"Nonlinear differential identities for cnoidal waves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Alice Mikikits-Leitner, Michael Leitner","submitted_at":"2013-08-05T09:41:32Z","abstract_excerpt":"This article presents a family of nonlinear differential identities for the spatially periodic function $u_s(x)$, which is essentially the Jacobian elliptic function $\\cn^2(z;m(s))$ with one non-trivial parameter $s$. More precisely, we show that this function $u_s$ fulfills equations of the form {equation*} \\big(u_s^{(\\alpha)}u_s^{(\\beta)}\\big)(x)=\\sum_{n=0}^{2+\\alpha+\\beta}b_{\\alpha,\\beta}(n)u_s^{(n)}(x)+c_{\\alpha,\\beta}, {equation*} for any $s>0$ and for all $\\alpha,\\beta\\in\\N_0$. We give explicit expressions for the coefficients $b_{\\alpha,\\beta}(n)$ and $c_{\\alpha,\\beta}$ for given $s$.\n "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.0920","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":""},"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"}