{"paper":{"title":"Bi-$\\cal{PT}$ symmetry in nonlinearly damped dynamical systems and tailoring $\\cal{PT}$ regions with position dependent loss-gain profiles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"nlin.PS","authors_text":"M. Lakshmanan, M. Senthilvelan, S. Karthiga, V.K. Chandrasekar","submitted_at":"2014-12-08T14:17:06Z","abstract_excerpt":"We investigate the remarkable role of position dependent damping in determining the parametric regions of symmetry breaking in nonlinear $\\cal{PT}$-symmetric systems. We illustrate the nature of $\\cal{PT}$-symmetry preservation and breaking with reference to a remarkable integrable scalar nonlinear system. In the two dimensional cases of such position dependent damped systems, we unveil the existence of a class of novel bi-$\\cal{PT}$-symmetric systems which have two fold $\\cal{PT}$ symmetries. We analyze the dynamics of these systems and show how symmetry breaking occurs, that is whether the s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.2574","kind":"arxiv","version":3},"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"}