{"paper":{"title":"The inverse problem of a mixed Li\\'enard type nonlinear oscillator equation from symmetry perspective","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.SI","authors_text":"Ajey K. Tiwari, M. Lakshmanan, M. Senthilvelan, S. N. Pandey, V. K. Chandrasekar","submitted_at":"2016-03-24T09:32:49Z","abstract_excerpt":"In this paper, we discuss the inverse problem for a mixed Li\\'enard type nonlinear oscillator equation $\\ddot{x}+f(x)\\dot{x}^2+g(x)\\dot{x}+h(x)=0$, where $f(x),\\,g(x)$ and $h(x)$ are arbitrary functions of $x$. Very recently, we have reported the Lie point symmetries of this equation. By exploiting the interconnection between Jacobi last multiplier, Lie point symmetries and Prelle-Singer procedure we construct a time independent integral for the case exhibiting maximal symmetry from which we identify the associated conservative non-standard Lagrangian and Hamiltonian functions. The classical d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.07496","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"}